<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema"><Version>2.2.0.25</Version><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><ReportLongName>1170 - Disclosure - Asset Retirement Obligations</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelColumn>false</LabelColumn><CurrencyCode>USD</CurrencyCode><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName>1/1/2010 - 12/31/2010
USD ($) / shares

USD ($)

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The following table provides a rollforward of the &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10.5pt;"&gt;Company's &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10.5pt;"&gt;combined short and long-term &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10.5pt;"&gt;ARO&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10.5pt;"&gt;s&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10.5pt;"&gt;. Liabilities settled include settlement payments for obligations&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10.5pt;"&gt;,&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10.5pt;"&gt; as well as obligations that were assumed by purchasers of divested properties. Revisions to estimated liabilities during the period relate primarily to changes in estimates of asset retirement costs and include, but are not limited to, revisions of estimated inflation rates, changes in property lives and the expected timing of settling &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10.5pt;"&gt;AROs&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10.5pt;"&gt;.&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top: 0pt; margin-bottom: 0pt;'&gt;&lt;/p&gt;&lt;div&gt;&lt;table style="border-collapse:collapse;margin-top:20px;"&gt;&lt;tr style="height: 1px"&gt;&lt;td   style="width: 530px; text-align:left;border-color:#000000;min-width:530px;"&gt;&amp;#160;&lt;sup&gt;&lt;/sup&gt;&lt;/td&gt;&lt;td   style="width: 10px; text-align:left;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 54px; text-align:left;border-color:#000000;min-width:54px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 10px; text-align:left;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 10px; text-align:left;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 54px; text-align:left;border-color:#000000;min-width:54px;"&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;&lt;tr style="height: 18px"&gt;&lt;td   style="width: 530px; text-align:left;border-color:#000000;min-width:530px;"&gt;&lt;font style="FONT-STYLE: italic;FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;"&gt;millions&lt;/font&gt;&lt;sup&gt;&lt;/sup&gt;&lt;/td&gt;&lt;td colspan="2"  style="width: 64px; border-bottom-style:solid;border-bottom-width:1px;text-align:center;border-color:#000000;min-width:64px;"&gt;&lt;font style="FONT-WEIGHT: bold;FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: center;"&gt;2010&lt;/font&gt;&lt;/td&gt;&lt;td   style="width: 10px; text-align:center;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td colspan="2"  style="width: 64px; border-bottom-style:solid;border-bottom-width:1px;text-align:center;border-color:#000000;min-width:64px;"&gt;&lt;font style="FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: center;"&gt;2009&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style="height: 18px"&gt;&lt;td   style="width: 530px; text-align:left;border-color:#000000;min-width:530px;"&gt;&lt;font style="FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;"&gt;Carrying amount of asset retirement obligations at January 1&lt;/font&gt;&lt;sup&gt;&lt;/sup&gt;&lt;/td&gt;&lt;td   style="width: 10px; border-top-style:solid;border-top-width:1px;text-align:center;border-color:#000000;min-width:10px;"&gt;&lt;font style="FONT-WEIGHT: bold;FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: center;"&gt;$&lt;/font&gt;&lt;/td&gt;&lt;td   style="width: 54px; border-top-style:solid;border-top-width:1px;text-align:right;border-color:#000000;min-width:54px;"&gt;&lt;font style="FONT-WEIGHT: bold;FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: right;"&gt;1,446&lt;/font&gt;&lt;/td&gt;&lt;td   style="width: 10px; text-align:left;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 10px; border-top-style:solid;border-top-width:1px;text-align:center;border-color:#000000;min-width:10px;"&gt;&lt;font style="FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: center;"&gt;$&lt;/font&gt;&lt;/td&gt;&lt;td   style="width: 54px; border-top-style:solid;border-top-width:1px;text-align:right;border-color:#000000;min-width:54px;"&gt;&lt;font style="FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: right;"&gt;1,368&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style="height: 18px"&gt;&lt;td   style="width: 530px; text-align:left;border-color:#000000;min-width:530px;"&gt;&lt;font style="FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;"&gt;Liabilities incurred&lt;/font&gt;&lt;sup&gt;&lt;/sup&gt;&lt;/td&gt;&lt;td   style="width: 10px; text-align:center;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 54px; text-align:right;border-color:#000000;min-width:54px;"&gt;&lt;font style="FONT-WEIGHT: bold;FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: right;"&gt;88&lt;/font&gt;&lt;/td&gt;&lt;td   style="width: 10px; text-align:left;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 10px; text-align:center;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 54px; text-align:right;border-color:#000000;min-width:54px;"&gt;&lt;font style="FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: right;"&gt;46&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style="height: 18px"&gt;&lt;td   style="width: 530px; text-align:left;border-color:#000000;min-width:530px;"&gt;&lt;font style="FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;"&gt;Liabilities settled&lt;/font&gt;&lt;sup&gt;&lt;/sup&gt;&lt;/td&gt;&lt;td   style="width: 10px; text-align:center;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 54px; text-align:right;border-color:#000000;min-width:54px;"&gt;&lt;font style="FONT-WEIGHT: bold;FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: right;"&gt;(36)&lt;/font&gt;&lt;/td&gt;&lt;td   style="width: 10px; text-align:left;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 10px; text-align:center;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 54px; text-align:right;border-color:#000000;min-width:54px;"&gt;&lt;font style="FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: right;"&gt;(54)&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style="height: 18px"&gt;&lt;td   style="width: 530px; text-align:left;border-color:#000000;min-width:530px;"&gt;&lt;font style="FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;"&gt;Accretion expense&lt;/font&gt;&lt;sup&gt;&lt;/sup&gt;&lt;/td&gt;&lt;td   style="width: 10px; text-align:center;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 54px; text-align:right;border-color:#000000;min-width:54px;"&gt;&lt;font style="FONT-WEIGHT: bold;FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: right;"&gt;92&lt;/font&gt;&lt;/td&gt;&lt;td   style="width: 10px; text-align:left;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 10px; text-align:center;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 54px; text-align:right;border-color:#000000;min-width:54px;"&gt;&lt;font style="FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: right;"&gt;89&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style="height: 18px"&gt;&lt;td   style="width: 530px; text-align:left;border-color:#000000;min-width:530px;"&gt;&lt;font style="FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;"&gt;Revisions in estimated liabilities&lt;/font&gt;&lt;sup&gt;&lt;/sup&gt;&lt;/td&gt;&lt;td   style="width: 10px; border-bottom-style:solid;border-bottom-width:1px;text-align:center;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 54px; border-bottom-style:solid;border-bottom-width:1px;text-align:right;border-color:#000000;min-width:54px;"&gt;&lt;font style="FONT-WEIGHT: bold;FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: right;"&gt;(19)&lt;/font&gt;&lt;/td&gt;&lt;td   style="width: 10px; text-align:left;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 10px; border-bottom-style:solid;border-bottom-width:1px;text-align:center;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 54px; border-bottom-style:solid;border-bottom-width:1px;text-align:right;border-color:#000000;min-width:54px;"&gt;&lt;font style="FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: right;"&gt;(3)&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style="height: 18px"&gt;&lt;td   style="width: 530px; text-align:left;border-color:#000000;min-width:530px;"&gt;&lt;font style="FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;"&gt;Carrying amount of asset retirement obligations at December 31&lt;/font&gt;&lt;sup&gt; (1)&lt;/sup&gt;&lt;/td&gt;&lt;td   style="width: 10px; border-top-style:solid;border-top-width:1px;border-bottom-style:solid;border-bottom-width:1px;text-align:center;border-color:#000000;min-width:10px;"&gt;&lt;font style="FONT-WEIGHT: bold;FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: center;"&gt;$&lt;/font&gt;&lt;/td&gt;&lt;td   style="width: 54px; border-top-style:solid;border-top-width:1px;border-bottom-style:solid;border-bottom-width:1px;text-align:right;border-color:#000000;min-width:54px;"&gt;&lt;font style="FONT-WEIGHT: bold;FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: right;"&gt;1,571&lt;/font&gt;&lt;/td&gt;&lt;td   style="width: 10px; text-align:left;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 10px; border-top-style:solid;border-top-width:1px;border-bottom-style:solid;border-bottom-width:1px;text-align:center;border-color:#000000;min-width:10px;"&gt;&lt;font style="FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: center;"&gt;$&lt;/font&gt;&lt;/td&gt;&lt;td   style="width: 54px; border-top-style:solid;border-top-width:1px;border-bottom-style:solid;border-bottom-width:1px;text-align:right;border-color:#000000;min-width:54px;"&gt;&lt;font style="FONT-FAMILY: Times New Roman;FONT-SIZE: 10.5pt;COLOR: #000000;TEXT-ALIGN: right;"&gt;1,446&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style="height: 1px"&gt;&lt;td   style="width: 530px; text-align:left;border-color:#000000;min-width:530px;"&gt;&amp;#160;&lt;sup&gt;&lt;/sup&gt;&lt;/td&gt;&lt;td   style="width: 10px; border-top-style:solid;border-top-width:1px;text-align:left;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 54px; border-top-style:solid;border-top-width:1px;text-align:left;border-color:#000000;min-width:54px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 10px; text-align:left;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 10px; border-top-style:solid;border-top-width:1px;text-align:left;border-color:#000000;min-width:10px;"&gt;&amp;#160;&lt;/td&gt;&lt;td   style="width: 54px; border-top-style:solid;border-top-width:1px;text-align:left;border-color:#000000;min-width:54px;"&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;/div&gt;&lt;p style='margin-top: 0pt; margin-bottom: 0pt;'&gt;&lt;/p&gt;&lt;p style='margin-top:12pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;margin-left:0px;"&gt;_________________________________________________________&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:0pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;margin-left:0px;"&gt;(1)&amp;#160;&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10.5pt;"&gt; &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;At &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;December 31, 2010&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt; and &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;2009&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;, &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;short&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;-term &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;ARO&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;s of $&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;42&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;&amp;#160;&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;m&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;illion &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;and $&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;31&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt; &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;m&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;illion, respectively, &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;were&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt; &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;presented in the Consolidated Balance Sheets&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt; as accrued expenses&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:9.5pt;"&gt;.&lt;/font&gt;&lt;/p&gt;</NonNumbericText><NonNumericTextHeader>10.&amp;#160;&amp;#160;Asset Retirement Obligations&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;The majority of Anadarko's AROs relate to the plugging and</NonNumericTextHeader><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>us-types:textBlockItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>Description of the asset retirement obligation and the associated long-lived asset. An asset retirement obligation is a legal obligation associated with the disposal or retirement from service of a tangible long-lived asset that results from the acquisition, construction or development, or the normal operations of a long-lived asset, except for certain obligations of lessees. This element may be used for all the disclosures related to asset retirement obligations.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name Statement of Financial Accounting Standard (FAS)
 -Number 143
 -Paragraph 22

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