<?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>1080 - Disclosure - ASSET RETIREMENT OBLIGATIONS</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

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</LabelSeparator><Level>2</Level><ElementName>us-gaap_AssetRetirementObligationDisclosureTextBlock</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="D2013Q2YTD" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="font-size:10.0pt;font-family:Times New Roman;"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&lt;b&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt; FONT-WEIGHT: bold;" size="2"&gt;8.&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; ASSET RETIREMENT OBLIGATIONS&lt;/font&gt;&lt;/b&gt;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;
&lt;p style="TEXT-INDENT: 0.25in; MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;We estimate the fair values of AROs based on historical experience of plug and abandonment costs by field and, assumptions and judgments regarding such factors as the existence of a legal obligation for an ARO; estimated probabilities, amounts and timing of settlements; the credit-adjusted risk-free rate to be used and inflation rates.&amp;#160; The following table sets forth the composition of asset retirement obligations rollforward:&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;
&lt;table style="text-align:left;WIDTH: 93.34%; BORDER-COLLAPSE: collapse; MARGIN-LEFT: 0.25in;" border="0" cellspacing="0" cellpadding="0" width="93%"&gt;

&lt;tr style="padding:0;"&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 83.4%; PADDING-RIGHT: 0in; BACKGROUND: #cceeff; PADDING-TOP: 0in;" bgcolor="#CCEEFF" valign="bottom" width="83%"&gt;
&lt;p style="TEXT-INDENT: -10pt; MARGIN: 0in 0in 0pt 10pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;Beginning January&amp;#160;1, 2013 liability&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 2.68%; PADDING-RIGHT: 0in; BACKGROUND: #cceeff; PADDING-TOP: 0in;" bgcolor="#CCEEFF" valign="bottom" width="2%"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 1.38%; PADDING-RIGHT: 0in; BACKGROUND: #cceeff; PADDING-TOP: 0in;" bgcolor="#CCEEFF" valign="bottom" width="1%"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;$&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 11.46%; PADDING-RIGHT: 0in; BACKGROUND: #cceeff; PADDING-TOP: 0in;" bgcolor="#CCEEFF" valign="bottom" width="11%"&gt;
&lt;p style="TEXT-ALIGN: right; MARGIN: 0in 0in 0pt;" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;11,029,206&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 1.08%; PADDING-RIGHT: 0in; BACKGROUND: #cceeff; PADDING-TOP: 0in;" bgcolor="#CCEEFF" valign="bottom" width="1%"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0;"&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 83.4%; PADDING-RIGHT: 0in; PADDING-TOP: 0in;" valign="bottom" width="83%"&gt;
&lt;p style="TEXT-INDENT: -10pt; MARGIN: 0in 0in 0pt 10pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;Accretion expense&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 2.68%; PADDING-RIGHT: 0in; PADDING-TOP: 0in;" valign="bottom" width="2%"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 12.86%; PADDING-RIGHT: 0in; PADDING-TOP: 0in;" valign="bottom" width="12%" colspan="2"&gt;
&lt;p style="TEXT-ALIGN: right; MARGIN: 0in 0in 0pt;" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;244,182&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 1.08%; PADDING-RIGHT: 0in; PADDING-TOP: 0in;" valign="bottom" width="1%"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0;"&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 83.4%; PADDING-RIGHT: 0in; BACKGROUND: #cceeff; PADDING-TOP: 0in;" bgcolor="#CCEEFF" valign="bottom" width="83%"&gt;
&lt;p style="TEXT-INDENT: -10pt; MARGIN: 0in 0in 0pt 10pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;Liabilities incurred&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 2.68%; PADDING-RIGHT: 0in; BACKGROUND: #cceeff; PADDING-TOP: 0in;" bgcolor="#CCEEFF" valign="bottom" width="2%"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 12.86%; PADDING-RIGHT: 0in; BACKGROUND: #cceeff; PADDING-TOP: 0in;" bgcolor="#CCEEFF" valign="bottom" width="12%" colspan="2"&gt;
&lt;p style="TEXT-ALIGN: right; MARGIN: 0in 0in 0pt;" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;16,727&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 1.08%; PADDING-RIGHT: 0in; BACKGROUND: #cceeff; PADDING-TOP: 0in;" bgcolor="#CCEEFF" valign="bottom" width="1%"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0;"&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 83.4%; PADDING-RIGHT: 0in; PADDING-TOP: 0in;" valign="bottom" width="83%"&gt;
&lt;p style="TEXT-INDENT: -10pt; MARGIN: 0in 0in 0pt 10pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;Liabilities settled&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 2.68%; PADDING-RIGHT: 0in; PADDING-TOP: 0in;" valign="bottom" width="2%"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 12.86%; PADDING-RIGHT: 0in; PADDING-TOP: 0in;" valign="bottom" width="12%" colspan="2"&gt;
&lt;p style="TEXT-ALIGN: right; MARGIN: 0in 0in 0pt;" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;(187,976&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 1.08%; PADDING-RIGHT: 0in; PADDING-TOP: 0in;" valign="bottom" width="1%"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;)&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0;"&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 83.4%; PADDING-RIGHT: 0in; BACKGROUND: #cceeff; PADDING-TOP: 0in;" bgcolor="#CCEEFF" valign="bottom" width="83%"&gt;
&lt;p style="TEXT-INDENT: -10pt; MARGIN: 0in 0in 0pt 10pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;Revisions&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 2.68%; PADDING-RIGHT: 0in; BACKGROUND: #cceeff; PADDING-TOP: 0in;" bgcolor="#CCEEFF" valign="bottom" width="2%"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;&lt;/td&gt;
&lt;td style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 12.86%; PADDING-RIGHT: 0in; BACKGROUND: #cceeff; BORDER-TOP: medium none; BORDER-RIGHT: medium none; PADDING-TOP: 0in;" bgcolor="#CCEEFF" valign="bottom" width="12%" colspan="2"&gt;
&lt;p style="TEXT-ALIGN: right; MARGIN: 0in 0in 0pt;" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;5,422&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 1.08%; PADDING-RIGHT: 0in; BACKGROUND: #cceeff; PADDING-TOP: 0in;" bgcolor="#CCEEFF" valign="bottom" width="1%"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0;"&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 83.4%; PADDING-RIGHT: 0in; PADDING-TOP: 0in;" valign="bottom" width="83%"&gt;
&lt;p style="TEXT-INDENT: -10pt; MARGIN: 0in 0in 0pt 10pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;Ending June&amp;#160;30, 2013 liability&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 2.68%; PADDING-RIGHT: 0in; PADDING-TOP: 0in;" valign="bottom" width="2%"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;&lt;/td&gt;
&lt;td style="BORDER-BOTTOM: windowtext 2.25pt double; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 1.38%; PADDING-RIGHT: 0in; BORDER-TOP: medium none; BORDER-RIGHT: medium none; PADDING-TOP: 0in;" valign="bottom" width="1%"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;$&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="BORDER-BOTTOM: windowtext 2.25pt double; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 11.46%; PADDING-RIGHT: 0in; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: medium none; PADDING-TOP: 0in;" valign="bottom" width="11%"&gt;
&lt;p style="TEXT-ALIGN: right; MARGIN: 0in 0in 0pt;" align="right"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;11,107,561&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; WIDTH: 1.08%; PADDING-RIGHT: 0in; PADDING-TOP: 0in;" valign="bottom" width="1%"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&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 an 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.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 410

 -SubTopic 20

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=6392692&amp;loc=d3e7535-110849



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

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 410

 -SubTopic 20

 -Section 50

 -Paragraph 2

 -URI http://asc.fasb.org/extlink&amp;oid=6392692&amp;loc=d3e7569-110849



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

 -Publisher FASB

 -Name Statement of Financial Accounting Standard (FAS)

 -Number 143

 -Paragraph 22

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



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