<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>11301 - Disclosure - Litigation, Other Contingencies and Guarantees</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>Duration_2_3_2013_To_8_3_2013</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001166126</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-02-03T00:00:00</PeriodStartDate><PeriodEndDate>2013-08-03T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Aug. 03, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>jcp_LitigationOtherContingenciesAndGuaranteesAbstract</ElementName><ElementPrefix>jcp_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Litigation, Other Contingencies and Guarantees [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_CommitmentsAndContingenciesDisclosureTextBlock</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="Duration_2_3_2013_To_8_3_2013" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div&gt; &lt;div style="margin-left:0pt;margin-right:0pt;"&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;font-weight:bold;"&gt;12.&amp;nbsp; &lt;/font&gt;&lt;a name="Litigation_Other_Contingencies_Guarantee"&gt;&lt;/a&gt;&lt;font style="display: inline;font-weight:bold;"&gt;Litigation&lt;/font&gt;&lt;font style="display: inline;font-weight:bold;"&gt;, Other Contingencies and Guarantees&lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;"&gt; &amp;nbsp; &lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;font-weight:bold;text-decoration:underline;"&gt;Litigation&amp;nbsp;&amp;nbsp; &lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;border-bottom:1pt none #D9D9D9 ;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;font-weight:bold;font-style:italic;font-size:10pt;"&gt;Macy&amp;#x2019;s Litigation&lt;/font&gt;&lt;font style="display: inline;font-size:10pt;"&gt;&amp;nbsp;&lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;border-top:1pt none #D9D9D9 ;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;font-size:10pt;"&gt;On August&lt;/font&gt;&lt;font style="display: inline;font-size:10pt;"&gt; 16, 2012, Macy&amp;#x2019;s, Inc. and Macy&amp;#x2019;s Merchandising Group, Inc. (together the Plaintiffs) filed suit against J. C. Penney Corporation, Inc. in the Supreme Court of the State of New York, County of New York, alleging that the Company tortiously interfered with, and engaged in unfair competition relating to a 2006 agreement between Macy&amp;#x2019;s and Martha Stewart Living Omnimedia, Inc. (MSLO) by entering into a partnership agreement with MSLO in December 2011.&amp;nbsp; The Plaintiffs seek primarily to prevent the Company from implementing our partnership agreement with MSLO as it relates to products in the bedding, bath, kitchen and cookware categories.&amp;nbsp; The suit was consolidated with an already-existing breach of contract lawsuit by the Plaintiffs against MSLO, and a bench trial commenced on February 20, 2013.&amp;nbsp; On March 7, 2013, the judge adjourned the trial until April 8, 2013, and ordered the parties into mediation.&amp;nbsp; The parties did not reach a settlement, and the trial continued on April 8, 2013.&amp;nbsp; The parties concluded their presentations of evidence on April 26, 2013, &lt;/font&gt;&lt;font style="display: inline;font-size:10pt;"&gt;and completed &lt;/font&gt;&lt;font style="display: inline;font-size:10pt;"&gt;post-trial briefs &lt;/font&gt;&lt;font style="display: inline;font-size:10pt;"&gt;&amp;nbsp;in late &lt;/font&gt;&lt;font style="display: inline;font-size:10pt;"&gt;May, 2013&lt;/font&gt;&lt;font style="display: inline;font-size:10pt;"&gt;.&amp;nbsp; The court held closing arguments on August 1, 2013.&amp;nbsp; The court has not yet issued a final decision in the case&lt;/font&gt;&lt;font style="display: inline;font-size:10pt;"&gt;.&amp;nbsp; While no assurance can be given as to the ultimate outcome of this matter, we currently believe that the final resolution of this action will not have a material adverse effect on our results of operations, financial position, liquidity or capital resources. &lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;"&gt; &amp;nbsp; &lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;

		&lt;/p&gt;
		&lt;p&gt;&lt;font size="1"&gt; &lt;/font&gt;&lt;/p&gt;&lt;p style="page-break-after:always"&gt;&amp;nbsp;&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;;font-size: 10pt"&gt;&lt;font style="display: inline;font-weight:bold;font-style:italic;"&gt;&lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;font-weight:bold;font-style:italic;"&gt;Other Legal Proceedings&lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;"&gt;We&lt;/font&gt;&lt;font style="display: inline;"&gt;&amp;nbsp;&lt;/font&gt;&lt;font style="display: inline;"&gt;are&lt;/font&gt;&lt;font style="display: inline;"&gt; subject to various legal and governmental proceedings involving routine litigation incidental to &lt;/font&gt;&lt;font style="display: inline;"&gt;our&lt;/font&gt;&lt;font style="display: inline;"&gt; business. Reserves have been established based on &lt;/font&gt;&lt;font style="display: inline;"&gt;our&lt;/font&gt;&lt;font style="display: inline;"&gt; best estimates of &lt;/font&gt;&lt;font style="display: inline;"&gt;our&lt;/font&gt;&lt;font style="display: inline;"&gt; potential liability in certain of these matters. These estimates have been developed in consultation with in-house and outside counsel. While no assurance can be given as to the ultimate outcome of these matters, management currently believes that the final resolution of these actions, individually or in the aggregate, will not have a material adverse effect on &lt;/font&gt;&lt;font style="display: inline;"&gt;our&lt;/font&gt;&lt;font style="display: inline;"&gt; results of operations, financial position, liquidity or capital resources&lt;/font&gt;&lt;font style="display: inline;"&gt;.&lt;/font&gt;&lt;font style="display: inline;"&gt;&amp;nbsp;&lt;/font&gt;&lt;font style="display: inline;"&gt; &amp;nbsp; &amp;nbsp;&lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;"&gt; &amp;nbsp; &lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;font-weight:bold;text-decoration:underline;"&gt;Contingencies&lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;"&gt;As of &lt;/font&gt;&lt;font style="display: inline;"&gt;August 3, 2013&lt;/font&gt;&lt;font style="display: inline;"&gt;, &amp;nbsp;&lt;/font&gt;&lt;font style="display: inline;"&gt;we&lt;/font&gt;&lt;font style="display: inline;"&gt; estimated &lt;/font&gt;&lt;font style="display: inline;"&gt;our&lt;/font&gt;&lt;font style="display: inline;"&gt; total potential environmental liabilities to range from &lt;/font&gt;&lt;font style="display: inline;"&gt;$&lt;/font&gt;&lt;font style="display: inline;"&gt;19&lt;/font&gt;&lt;font style="display: inline;"&gt; million to &lt;/font&gt;&lt;font style="display: inline;"&gt;$&lt;/font&gt;&lt;font style="display: inline;"&gt;25&lt;/font&gt;&lt;font style="display: inline;"&gt; million and&lt;/font&gt;&lt;font style="display: inline;"&gt; recorded our best estimate of &lt;/font&gt;&lt;font style="display: inline;"&gt;$&lt;/font&gt;&lt;font style="display: inline;"&gt;20&lt;/font&gt;&lt;font style="display: inline;"&gt; million in other liabilities in the unaudited Consolidated Balance Sheet as of that date. This estimate covered potential liabilities primarily related to underground storage tanks, remediation of environmental conditions involving our former drugstore locations and asbestos removal in connection with approved plans to renovate or dispose of our facilities. We continue to assess required remediation and the adequacy of environmental reserves as new information becomes available and known conditions are further delineated. If we were to incur losses at the upper end of the estimated range, we do not believe that such losses would have &lt;/font&gt;&lt;font style="display: inline;"&gt;a material adverse effect on our results of operations, financial position, liquidity or capital resources.&lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;"&gt; &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;font-weight:bold;text-decoration:underline;"&gt;Guarantees&lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;"&gt;As of &lt;/font&gt;&lt;font style="display: inline;"&gt;August 3, 2013&lt;/font&gt;&lt;font style="display: inline;"&gt;,&lt;/font&gt;&lt;font style="display: inline;"&gt; we had a guarantee totaling $&lt;/font&gt;&lt;font style="display: inline;"&gt;20&lt;/font&gt;&lt;font style="display: inline;"&gt;&amp;nbsp;&lt;/font&gt;&lt;font style="display: inline;"&gt;million&lt;/font&gt;&lt;font style="display: inline;"&gt; for the &lt;/font&gt;&lt;font style="display: inline;"&gt;maximum exposure on insurance reserves established by a former subsidiary included in the sale of &lt;/font&gt;&lt;font style="display: inline;"&gt;our&lt;/font&gt;&lt;font style="display: inline;"&gt; Direct Marketing Services business&lt;/font&gt;&lt;font style="display: inline;"&gt;.&lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;"&gt; &amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;"&gt;In connection with the sale of the operations of our outlet stores, we assigned leases on 7 outlet store locations to the purchaser.&amp;nbsp; In the event that the purchaser fails to make the required lease payments, we continue for a period of time to be liable for lease payments to each landlord of the 7 assigned leases.&amp;nbsp; The purchaser&amp;#x2019;s obligations under the leases are guaranteed to us by certain principals and affiliates of the purchaser. &amp;nbsp;We are currently engaged in discussions regarding restructuring the agreement.&amp;nbsp; A&lt;/font&gt;&lt;font style="display: inline;"&gt;s of &lt;/font&gt;&lt;font style="display: inline;"&gt;August 3, 2013, o&lt;/font&gt;&lt;font style="display: inline;"&gt;ur maximum liability in connection with the assigned leases is $&lt;/font&gt;&lt;font style="display: inline;"&gt;10&lt;/font&gt;&lt;font style="display: inline;"&gt;&amp;nbsp;&lt;/font&gt;&lt;font style="display: inline;"&gt;million.&amp;nbsp; &amp;nbsp;&lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;"&gt; &amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/font&gt;
		&lt;/p&gt;
		&lt;p style="margin:0pt;font-family:Times New Roman;font-size: 10pt"&gt;
			&lt;font style="display: inline;"&gt;In connection with the redemption of two million of our SPG REIT units, we agreed to make future capital contributions to SPG under certain circumstances.&amp;nbsp;&amp;nbsp;&lt;/font&gt;&lt;font style="display: inline;"&gt;Capital contributions would be required only if (i) one or more unsecured senior notes or term loans of SPG are in default and (ii) the aggregate amount received and/or realized by the lenders with respect to such notes or loans upon the exhaustion of all other remedies available to them is less than the maximum amount of all capital contribution commitments of the Company and other parties with similar commitments.&amp;nbsp;&amp;nbsp;&lt;/font&gt;&lt;font style="display: inline;"&gt;Our contribution obligation is subject to a maximum aggregate amount of $&lt;/font&gt;&lt;font style="display: inline;"&gt;360&lt;/font&gt;&lt;font style="display: inline;"&gt; million, and is proportionate to our share of all similar commitments provided by the Company and other parties. &lt;/font&gt;&lt;font style="display: inline;"&gt; Under certain circumstances, including the disposition of its remaining SPG REIT units, the Company can terminate its obligation.&amp;nbsp; &lt;/font&gt;&lt;font style="display: inline;"&gt;The possibility that we would be required to make a contribution is considered remote, and as such, no amount has been recorded in the unaudited Interim Consolidated Financial Statements.&lt;/font&gt;
		&lt;/p&gt;
		&lt;p&gt;&lt;font size="1"&gt; &lt;/font&gt;&lt;/p&gt;
	&lt;/div&gt; &lt;/div&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>The entire disclosure for commitments and contingencies.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 210

 -SubTopic 10

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.5-02.25)

 -URI http://asc.fasb.org/extlink&amp;oid=6877327&amp;loc=d3e13212-122682



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 825

 -SubTopic 20

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=6449706&amp;loc=d3e16207-108621



Reference 3: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 460

 -SubTopic 10

 -Section 50

 -Paragraph 8

 -URI http://asc.fasb.org/extlink&amp;oid=6398077&amp;loc=d3e12565-110249



Reference 4: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 450

 -SubTopic 20

 -Section 50

 -Paragraph 4

 -URI http://asc.fasb.org/extlink&amp;oid=25496072&amp;loc=d3e14435-108349



Reference 5: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 440

 -SubTopic 10

 -Section 50

 -Paragraph 2

 -URI http://asc.fasb.org/extlink&amp;oid=6394976&amp;loc=d3e25287-109308



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Litigation, Other Contingencies and Guarantees</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Litigation, Other Contingencies and Guarantees</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.jcpenney.net/role/DisclosureLitigationOtherContingenciesAndGuarantees</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
