<?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>0210 - Disclosure - Legal Proceedings</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>1/1/2011 - 3/31/2011
USD ($)

USD ($) / shares
</KeyName><CurrencySymbol>$</CurrencySymbol><contextRef><ContextID>Jan-01-2011_Mar-31-2011</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000721683</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2011-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2011-03-31T00:00:00</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="3 Months Ended" /><Label Id="2" Label="Mar. 31, 2011" /></Labels></Column></Columns><Rows><Row><Id>2</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><Level>0</Level><ElementName>tss_LegalProceedingsAbstract</ElementName><ElementPrefix>tss</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><ShortDefinition>Legal proceedings.</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>Legal proceedings.</ElementDefenition><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>Legal Proceedings [Abstract]</Label></Row><Row><Id>3</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><Level>0</Level><ElementName>us-gaap_LegalCostsPolicyTextBlock</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 10 - us-gaap:LegalCostsPolicyTextBlock--&gt;
   &lt;div style="font-family: 'Times New Roman',Times,serif"&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 12pt"&gt;&lt;b&gt;Note 10 &amp;#8212; Legal Proceedings&lt;/b&gt;
   &lt;/div&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&lt;i&gt;General&lt;/i&gt;
   &lt;/div&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;The Company is subject to various legal proceedings and claims and is also subject to
   information requests, inquiries and investigations arising out of the ordinary conduct of its
   business. The Company establishes reserves for litigation and similar matters when those matters
   present loss contingencies that TSYS determines to be both probable and reasonably estimable in
   accordance with ASC 450, &amp;#8220;Contingencies.&amp;#8221; In the opinion of management, based on current knowledge
   and in part upon the advice of legal counsel, all matters not specifically discussed below are
   believed to be adequately covered by insurance, or if not covered, are believed to be without merit
   or are of such kind or involve such amounts that would not have a material adverse effect on the
   financial position, results of operations or cash flows of the Company if disposed of unfavorably.
   &lt;/div&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 12pt"&gt;&lt;i&gt;Infonox Matter&lt;/i&gt;
   &lt;/div&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;On April&amp;#160;29, 2011, TSYS entered into an agreement with Safwan Shah, both individually and in
   his capacity as a representative of certain remaining shareholders (the &amp;#8220;Agreement&amp;#8221;) to resolve all
   claims against Total System Services, Inc., TSYS Acquiring Solutions, L.L.C. and Infonox, a TSYS
   company, alleged in the previously disclosed litigation initiated by Mr.&amp;#160;Shah in the Superior Court
   of California, Santa Clara County (Case No.&amp;#160;1-10-CV-183173). Such claims arose out of TSYS&amp;#8217;
   purchase of Infonox on the Web (&amp;#8220;Infonox&amp;#8221;) in November&amp;#160;2008. The Agreement provides for the
   payment by TSYS of $6 million of contingent merger consideration to Mr.&amp;#160;Shah and the other remaining shareholders
   pursuant to the Agreement and Plan of Merger entered into in connection with the transaction and
   also provides for the dismissal of the litigation with prejudice and the mutual release of all
   parties to the litigation. The payment of the contingent merger consideration by TSYS will be
   recorded as goodwill and will have no impact on TSYS&amp;#8217; results of operations.
   &lt;/div&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 12pt"&gt;&lt;i&gt;Electronic Payment Systems Matter&lt;/i&gt;
   &lt;/div&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;In February&amp;#160;2007, TSYS Acquiring Solutions, L.L.C., a wholly owned subsidiary of TSYS (&amp;#8220;TSYS
   Acquiring&amp;#8221;), filed a demand for arbitration for payment of past due processing fees pursuant to a
   contract with Electronic Payment Systems LLC (&amp;#8220;EPS&amp;#8221;), an acquiring independent sales organization.
   EPS counterclaimed and alleged certain monetary damages. In April&amp;#160;2008, EPS amended its
   counterclaims, adding a claim for a declaration that the arbitrator award EPS ownership, control
   and access to the 1-800 number that connects EPS&amp;#8217; merchants to TSYS Acquiring as EPS&amp;#8217; processor. On
   January&amp;#160;20, 2009, the arbitrator denied all TSYS Acquiring&amp;#8217;s claims, awarded EPS approximately $3.3
   million in damages and fees and awarded EPS immediate ownership, control and access over the 1-800
   number.
   &lt;/div&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;On January&amp;#160;26, 2009, TSYS Acquiring filed an action (the &amp;#8220;First Action&amp;#8221;) in the United States
   District Court for the District of Arizona (Civil Action No.&amp;#160;CV09-00155-PHX-JAT) seeking to vacate
   the arbitration award. However, on October&amp;#160;22, 2009, the court granted summary judgment in favor of
   EPS. On May&amp;#160;4, 2010, after the court denied post-judgment motions filed by TSYS Acquiring, the
   court confirmed the monetary judgment and TSYS Acquiring paid the monetary judgment to EPS. TSYS
   Acquiring had been using seven 1-800 numbers to connect EPS&amp;#8217; merchants and the court interpreted
   the arbitrator&amp;#8217;s award to include all seven numbers.
   &lt;/div&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;On May&amp;#160;14, 2010, TSYS Acquiring filed a second action (the &amp;#8220;Second Action&amp;#8221;) in the United
   States District Court for the District of Arizona (Civil Action No.&amp;#160;CV10-01060-PHX-DGC) seeking a
   declaratory judgment that TSYS did not need to give EPS ownership and control of the seven 1-800
   numbers. EPS filed a motion for summary judgment on the request for declaratory relief. EPS also
   filed a counterclaim arguing that TSYS Acquiring should be required to pay EPS for its continued
   use of the 1-800 number and seeking punitive damages based on various consumer protection statutes.
   On November&amp;#160;9, 2010, the court granted EPS&amp;#8217; motion for summary judgment. The EPS counterclaims that
   were not previously dismissed in the Second Action remain pending.
   &lt;/div&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;On December&amp;#160;3, 2010, EPS filed a motion to compel in the First Action seeking to require TSYS
   Acquiring to provide EPS with immediate ownership, control and access over the seven 1-800 numbers
   used by EPS merchants.
   &lt;/div&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;On January&amp;#160;24, 2011, TSYS Acquiring filed a petition with the Federal Communications
   Commission (&amp;#8220;FCC&amp;#8221;) seeking a ruling that the enforcement of the arbitration award regarding the
   1-800 numbers would violate the FCC&amp;#8217;s rules regarding the allocation and transfer of 1-800 numbers.
   &lt;/div&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;On February&amp;#160;15, 2011, the court in the First Action issued an order (the &amp;#8220;Order&amp;#8221;) requiring
   TSYS Acquiring to comply with the arbitration award by moving all non-EPS merchants off of 1-800
   numbers used by EPS merchants, and to then transfer to EPS the seven toll free numbers at issue.
   The Order requires compliance within 90&amp;#160;days. In addition, the court rejected TSYS Acquiring&amp;#8217;s
   arguments that the award cannot be enforced because it violates FCC regulations.
   &lt;/div&gt;
   &lt;!-- Folio --&gt;
   &lt;!-- /Folio --&gt;
   &lt;/div&gt;
   &lt;!-- PAGEBREAK --&gt;
   &lt;div style="font-family: 'Times New Roman',Times,serif"&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;On February&amp;#160;24, 2011, the FCC released a Declaratory Ruling granting TSYS Acquiring&amp;#8217;s petition
   by affirming that the FCC has exclusive jurisdiction over the transfer of toll free numbers, and
   noting that several aspects of the arbitrator&amp;#8217;s ruling and the affirmation of that ruling by the
   United States District Court for the District of Arizona conflicted with the FCC&amp;#8217;s rules and
   related tariffs governing the transfer of toll free numbers. Because of this, the Declaratory
   Ruling proceeded to direct those third parties charged with the administration of the seven toll
   free numbers for TSYS Acquiring, as well as the Toll Free Number Administrator charged with
   administering the database of toll free numbers, to reject any requests seeking a transfer of those
   numbers from TSYS Acquiring to another party, absent a specific directive from the FCC.
   &lt;/div&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;Following the FCC&amp;#8217;s Declaratory Ruling that the toll free numbers may not be transferred by an
   order of the court or the arbitrator, TSYS Acquiring filed a motion for reconsideration with the
   United States District Court of the District of Arizona with respect to the Order. On April&amp;#160;8,
   2011, the United States District Court for the District of Arizona denied TSYS Acquiring&amp;#8217;s motion
   but granted a stay of enforcement of the Order pending EPS&amp;#8217; appeal of the FCC&amp;#8217;s Declaratory Ruling.
   Therefore, TSYS Acquiring is not required to comply with the Order within the 90-day time frame
   initially imposed by the court and does not intend to comply with the Order unless and until such
   time as is required by the court.
   &lt;/div&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;In light of the FCC&amp;#8217;s Declaratory Ruling that the toll free numbers may not be transferred by
   an order of the court or the arbitrator, TSYS Acquiring intends to continue to vigorously defend
   itself against any future enforcement of the Order in the United States District Court for the
   District of Arizona, and if necessary, the Ninth Circuit Court of Appeals.
   &lt;/div&gt;
   &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;If the Order is not ultimately vacated or modified in response to the FCC&amp;#8217;s Declaratory
   Ruling, or if EPS is successful in it&amp;#8217;s appeal of the FCC&amp;#8217;s Declaratory Ruling, it would require
   TSYS Acquiring to move over 750,000 merchants that use one of the seven numbers that EPS seeks to
   possess to other toll free numbers. TSYS Acquiring cannot estimate the cost of such compliance, but
   TSYS Acquiring believes the cost of such compliance would be substantial. However, we are unable to
   estimate the potential loss or range of losses at this time. Based upon current knowledge, TSYS&amp;#8217;
   management does not believe that the eventual outcome of this case will have a material adverse
   effect on TSYS&amp;#8217; financial position, results of operations or cash flows. However, it is possible
   that the ultimate outcome of this case may be material to TSYS&amp;#8217; results of operations for any
   particular period.
   &lt;/div&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>Describes an entity's accounting policy for legal costs incurred to protect or defend the entity's assets and rights, or to obtain assets, including monetary damages, or to obtain rights.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef
 -Publisher AICPA
 -Name Accounting Principles Board Opinion (APB)
 -Number 22
 -Paragraph 8

</ElementReferences><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>Legal Proceedings</Label></Row></Rows><Footnotes /><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows><ReportName>Legal Proceedings</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>false</HasCustomUnits><SharesShouldBeRounded>true</SharesShouldBeRounded></InstanceReport>
