<?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>106 - Disclosure - Goodwill and Intangible Assets</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-2013-01-01-to-2013-06-30.1661.0.0.0.0.0.0.0</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001034760</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_GoodwillAndIntangibleAssetsDisclosureAbstract</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>Goodwill and Intangible Assets [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_GoodwillDisclosureTextBlock</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>verboseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="from-2013-01-01-to-2013-06-30.1661.0.0.0.0.0.0.0" UnitID=""><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;div&gt; &lt;div&gt;&lt;!--StartFragment--&gt; &lt;table style="MARGIN-BOTTOM: 0pt; FONT: bold 10pt Times New Roman, Times, Serif; MARGIN-TOP: 0pt" cellspacing="0" cellpadding="0" width="100%"&gt; &lt;tr style="VERTICAL-ALIGN: top"&gt; &lt;td style="WIDTH: 0px"&gt;&amp;nbsp;&lt;/td&gt; &lt;td style="WIDTH: 0.25in"&gt;6.&lt;/td&gt; &lt;td&gt;Goodwill and Intangible Assets&lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;p style="MARGIN-BOTTOM: 0pt; FONT: 10pt Times New Roman, Times, Serif; MARGIN-TOP: 0pt"&gt; &amp;nbsp;&lt;/p&gt; &lt;p style="TEXT-ALIGN: justify; FONT: 10pt Times New Roman, Times, Serif; MARGIN: 0pt 0px; TEXT-INDENT: 0.25in"&gt; There were no changes in the carrying amount of goodwill for the three or six month periods ended June 30, 2013. We have not identified any quantitative or qualitative factors for goodwill that would indicate impairment exists at June 30, 2013.&lt;/p&gt; &lt;p style="TEXT-ALIGN: justify; FONT: 10pt Times New Roman, Times, Serif; MARGIN: 0pt 0px"&gt; &amp;nbsp;&lt;/p&gt; &lt;p style="TEXT-ALIGN: justify; FONT: 10pt Times New Roman, Times, Serif; MARGIN: 0pt 0px; TEXT-INDENT: 0.25in"&gt; The Company also has material intangible assets consisting of purchased intangibles and internally developed software used in the conduct of business. There were no additions to or disposals of intangible assets for the three or six month period ended June 30, 2013.&lt;/p&gt; &lt;p style="TEXT-ALIGN: justify; FONT: 10pt Times New Roman, Times, Serif; MARGIN: 0pt 0px; TEXT-INDENT: 0.25in"&gt; &amp;nbsp;&lt;/p&gt; &lt;p style="TEXT-ALIGN: justify; FONT: 10pt Times New Roman, Times, Serif; MARGIN: 0pt 0px; TEXT-INDENT: 0.3in"&gt; The aggregate amortization expense recorded for the three month periods ended June 30, 2013 and 2012 was approximately $336,900 and $390,200, respectively. The aggregate amortization expense recorded for the six month periods ended June 30, 2013 and 2012 was approximately $688,700 and $780,400, respectively. The total weighted average life of purchased and internally developed intangible assets is approximately 5.5 years at June 30, 2013.&lt;/p&gt; &lt;p style="FONT: 10pt Times New Roman, Times, Serif; MARGIN: 0pt 0px"&gt; &lt;strong&gt;&amp;nbsp;&lt;/strong&gt;&lt;/p&gt; &lt;!--EndFragment--&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 goodwill.</ElementDefenition><ElementReferences>No definition available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Goodwill and Intangible Assets</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Goodwill and Intangible Assets</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.widepoint.com/role/GoodwillAndIntangibleAssets</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
