<?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>001190 - Disclosure - Credit Agreements</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>FROM_Jan01_2013_TO_Jun30_2013</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000911421</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</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="Jun. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>us-gaap_LineOfCreditFacilityAbstract</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><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>Disclosure - Credit Agreements [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_ScheduleOfLineOfCreditFacilitiesTextBlock</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><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="FROM_Jan01_2013_TO_Jun30_2013" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;p style='margin-top:6pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-weight:bold;margin-left:0px;"&gt;9&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-weight:bold;"&gt;. Credit Agreements&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:9pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:24.5px;"&gt;In the normal course of its operations, the Company enters into agreements with financial institutions to obtain unsecured and secured credit facilities. These facilities are used primarily for the issuance of letters of credit, although a portion of these facilities may also be used for liquidity purposes.&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:9pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:24.5px;"&gt;On April&amp;#160;18, 2013, the Company modified its existing three-year syndicated unsecured credit facility to reduce the available facility from $500 million to $50 million and reduce its access to a revolving line of credit from $375 million to $50 million. All other terms remained unchanged. &lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:9pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:24.5px;"&gt;See Note 18 to the Consolidated Financial Statements included in the Company's Annual Report on Form 10-K for the year ended December&amp;#160;31, 2012 for further information related to the credit facilities available to the Company.&lt;/font&gt;&lt;/p&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>Tabular disclosure of short-term or long-term contractual arrangements with lenders, including letters of credit, standby letters of credit, and revolving credit arrangements, under which borrowings can be made up to maximum amount as of any point in time conditional on satisfaction of specified terms before, as of and after the date of drawdowns on the line.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 235

 -SubTopic 10

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.4-08.(e),(f))

 -URI http://asc.fasb.org/extlink&amp;oid=6881521&amp;loc=d3e23780-122690



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

 -Publisher SEC

 -Name Regulation S-X (SX)

 -Number 210

 -Section 08

 -Paragraph f

 -Article 4



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

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 210

 -SubTopic 10

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.5-02.19(b),22(b))

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



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

 -Publisher SEC

 -Name Regulation S-X (SX)

 -Number 210

 -Section 02

 -Paragraph 19, 22

 -Article 5



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Schedule Of Line Of Credit Facilities Text Block</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Credit Agreements</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.partnerre.com/role/DisclosureCreditAgreements</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
