<?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>0203 - Disclosure - Acquisitions of Businesses</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 ($)

USD ($) / shares
</KeyName><CurrencySymbol>$</CurrencySymbol><contextRef><ContextID>Jan-01-2010_Dec-31-2010</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000105634</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2010-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2010-12-31T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS><UnitProperty><UnitID>USD</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace></StandardMeasure><Scale>0</Scale></UnitProperty><UnitProperty><UnitID>USDEPS</UnitID><UnitType>Divide</UnitType><NumeratorMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace></NumeratorMeasure><DenominatorMeasure><MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema><MeasureValue>shares</MeasureValue><MeasureNamespace>xbrli</MeasureNamespace></DenominatorMeasure><Scale>0</Scale></UnitProperty></UPS><CurrencyCode>USD</CurrencyCode><OriginalCurrencyCode>USD</OriginalCurrencyCode></MCU><CurrencySymbol>$</CurrencySymbol><Labels><Label Id="1" Label="12 Months Ended" /><Label Id="2" Label="Dec. 31, 2010" /></Labels></Column></Columns><Rows><Row><Id>2</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><Level>0</Level><ElementName>eme_AcquisitionsOfBusinessesAbstract</ElementName><ElementPrefix>eme</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><ShortDefinition>No definition available.</ShortDefinition><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsSubReportEnd>false</IsSubReportEnd><IsCalendarTitle>false</IsCalendarTitle><IsTuple>false</IsTuple><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole /><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><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>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>No definition available.</ElementDefenition><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>Acquisitions of Businesses [Abstract]</Label></Row><Row><Id>3</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><Level>0</Level><ElementName>us-gaap_BusinessCombinationDisclosureTextBlock</ElementName><ElementPrefix>us-gaap</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><ShortDefinition>No definition available.</ShortDefinition><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsSubReportEnd>false</IsSubReportEnd><IsCalendarTitle>false</IsCalendarTitle><IsTuple>false</IsTuple><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>verboselabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
   &lt;!-- Begin Block Tagged Note 3 - us-gaap:BusinessCombinationDisclosureTextBlock--&gt;
   &lt;div style="margin-left: 0%"&gt;
   &lt;div style="margin-top: 18pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;table width="100%" border="0" cellpadding="0" cellspacing="0" style="font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: transparent; text-align: left"&gt;
   &lt;tr&gt;
       &lt;td width="8%"&gt;&lt;/td&gt;
       &lt;td width="92%"&gt;&lt;/td&gt;
   &lt;/tr&gt;
   &lt;tr valign="top"&gt;
       &lt;td&gt;
       &lt;b&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;NOTE&amp;#160;3&amp;#8212;&lt;/font&gt;&lt;/b&gt;
   &lt;/td&gt;
       &lt;td&gt;
       &lt;b&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;ACQUISITIONS
       OF BUSINESSES&lt;/font&gt;&lt;/b&gt;
   &lt;/td&gt;
   &lt;/tr&gt;
   &lt;/table&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 3%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       We acquired two companies during 2010 and a company in 2009,
       each for an immaterial amount. One of the companies acquired in
       2010 and the company acquired in 2009 provide mobile mechanical
       services, and the other company acquired in 2010 primarily
       performs government infrastructure contracting services. All of
       these companies have been included in our United States
       facilities services reporting segment.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 3%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       During 2008, we acquired five companies, which were not material
       individually or in the aggregate, for an aggregate of
       $82.7&amp;#160;million. One of the companies primarily provides
       industrial services to refineries, another primarily provides
       industrial maintenance services, and two others primarily
       perform mobile mechanical services. The results of these four
       companies have been included in our United States facilities
       services reporting segment. The fifth company is a fire
       protection company that has been included in our United States
       mechanical construction and facilities services reporting
       segment. Goodwill and identifiable intangible assets
       attributable to these five companies were valued at an aggregate
       of $15.0&amp;#160;million and $48.8&amp;#160;million, respectively,
       representing the excess of the aggregate purchase price over the
       fair value amounts assigned to their net tangible assets. See
       Note&amp;#160;8&amp;#8212;Goodwill and Identifiable Intangible Assets of
       the notes to consolidated financial statements for additional
       information.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 3%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       We believe the aforementioned acquisitions further our goal of
       service and geographic diversification
       &lt;font style="white-space: nowrap"&gt;and/or&lt;/font&gt;
       expansion of our facilities services operations and our
       mechanical construction and facilities services operation in our
       fire protection offerings. Additionally, these acquisitions
       create more opportunities for our subsidiaries to collaborate on
       national facilities services contracts.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 3%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       The purchase price allocation for one of our 2010 acquired
       companies is subject to the finalization of valuation of
       acquired identifiable intangible assets. The purchase price
       accounting for the other acquisitions referred to above was
       finalized. As a result, identifiable intangible assets ascribed
       to goodwill, contract backlog, customer relationships, trade
       names and related non-competition agreements were adjusted with
       an insignificant impact. These acquisitions were accounted for
       by the purchase method in 2008 and by the acquisition method in
       2010 and 2009, and the purchase prices for them have been
       allocated to their respective assets and liabilities, based upon
       the estimated fair values of the respective assets and
       liabilities at the dates of the respective acquisitions.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 3%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       For the year ended December&amp;#160;31, 2009, we recorded
       approximately $2.0&amp;#160;million of non-cash compensation expense
       related to a prior acquisition, with an offsetting amount
       recorded as a capital contribution from the selling shareholders
       of the acquired company. This non-cash expense was a result of a
       redistributed portion of acquisition-related payments made by
       the former owners of the acquired company to certain employees.
       These employees were not shareholders of the acquired company,
       and such payments were dependent on continuing employment with
       us.
   &lt;/div&gt;
   &lt;!-- XBRL Pagebreak Begin --&gt;
   &lt;/div&gt;
   &lt;!-- END PAGE WIDTH --&gt;
   &lt;!-- PAGEBREAK --&gt;
   &lt;div style="margin-left: 0%"&gt;
   &lt;!-- BEGIN PAGE WIDTH --&gt;
   &lt;div align="center" style="margin-left: 0%; margin-right: 0%; font-size: 12pt; font-family: Arial, Helvetica; color: #000000; background: transparent"&gt;
   &lt;b&gt;
   &lt;font style="font-family: 'Times New Roman', Times"&gt;
   &lt;font style="font-size: 10pt"&gt;
   &lt;/font&gt;
   &lt;/font&gt;
   &lt;/b&gt;
   &lt;/div&gt;
   &lt;div style="margin-top: 0pt; font-size: 1pt"&gt;
   &lt;/div&gt;
   &lt;!-- XBRL Pagebreak End --&gt;
   &lt;/div&gt;
</NonNumbericText><NonNumericTextHeader>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
   &lt;!-- Begin Block Tagged Note</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 a business combination (or series of individually immaterial business combinations) completed during the period, including background, timing, and recognized assets and liabilities. This element may be used as a single block of text to encapsulate the entire disclosure (including data and tables) regarding business combinations, including leverage buyout transactions (as applicable).</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name Statement of Financial Accounting Standard (FAS)
 -Number 141
 -Paragraph 51, 52

Reference 2: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name Emerging Issues Task Force (EITF)
 -Number 88-16

Reference 3: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name Statement of Financial Accounting Standard (FAS)
 -Number 141R
 -Paragraph 67-73

Reference 4: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name Statement of Financial Accounting Standard (FAS)
 -Number 141R
 -Paragraph F4
 -Subparagraph e
 -Appendix F

</ElementReferences><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>ACQUISITIONS OF BUSINESSES</Label></Row></Rows><Footnotes /><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows><ReportName>Acquisitions of Businesses</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>false</HasCustomUnits><SharesShouldBeRounded>true</SharesShouldBeRounded></InstanceReport>
