<?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>0212 - Disclosure - Share Repurchase Programs</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

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    &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 12 - us-gaap:ScheduleOfTreasuryStockByClassTextBlock--&gt;
    &lt;div style="font-family: 'Times New Roman',Times,serif"&gt;
    &lt;div align="left" style="font-size: 10pt; margin-top: 6pt; margin-left: 1%"&gt;&lt;b&gt;12. Share Repurchase Programs&lt;/b&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;As of January&amp;#160;19, 2010, the Company completed its $750&amp;#160;million share repurchase program that
    was announced on July&amp;#160;27, 2009, after repurchasing an additional 1.1&amp;#160;million shares in January&amp;#160;2010
    for $90&amp;#160;million at an average purchase price of $78.36 per share. In February&amp;#160;2010, the Board of
    Directors authorized the repurchase of up to $250&amp;#160;million of the Company&amp;#8217;s common stock, which was
    completed on May&amp;#160;26, 2010, after repurchasing 3.3&amp;#160;million shares at an average purchase price of
    $76.29 per share.
    &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 August&amp;#160;2010, Lorillard, Inc. announced that its Board of Directors had approved a new share
    repurchase program authorizing the Company to repurchase in the aggregate up to $1&amp;#160;billion of its
    outstanding common stock. Purchases by the Company under this program may be made from time to time
    at prevailing market prices in open market purchases, privately negotiated transactions, block
    purchases or otherwise, as determined by the Company&amp;#8217;s management. The repurchases are funded from
    existing cash balances, including proceeds from the Company&amp;#8217;s April&amp;#160;2010 issuance of the Notes (see
    Note 8 for a description of the Notes).
    &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;This program does not obligate the Company to acquire any particular amount of common stock.
    The timing, frequency and amount of repurchase activity will depend on a variety of factors such as
    levels of cash generation from operations, cash requirements for investment in the Company&amp;#8217;s
    business, current stock price, market conditions and other factors. The share repurchase program
    may be suspended, modified or discontinued at any time and has no set expiration date. During the
    first quarter of 2011, the Company repurchased approximately 3.8&amp;#160;million shares of its common stock
    at an average price of $76.76 per share, for a total of $289&amp;#160;million. As of March&amp;#160;31, 2011, the
    maximum value of shares that could yet be repurchased under the program was $335&amp;#160;million.
    &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;As of March&amp;#160;31, 2011, total shares repurchased under share repurchase programs authorized by
    the Board since the Separation were as follows:
    &lt;/div&gt;
    &lt;div align="center"&gt;
    &lt;table style="font-size: 10pt; text-align: left" cellspacing="0" border="0" cellpadding="0" width="100%"&gt;
    &lt;!-- Begin Table Head --&gt;
    &lt;tr valign="bottom"&gt;
    &lt;td width="4%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td width="18%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td width="1%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td width="5%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td width="1%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td width="15%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td width="7%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td width="15%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td width="7%"&gt;&amp;#160;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr style="font-size: 8pt" valign="bottom"&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" align="center"&gt;Number of&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr style="font-size: 8pt" valign="bottom"&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" align="center" colspan="2"&gt;Amount&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" align="center"&gt;Shares&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr style="font-size: 8pt" valign="bottom"&gt;
    &lt;td nowrap="nowrap" align="center" style="border-bottom: 1px solid #000000"&gt;Authorized&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" align="center" colspan="2" style="border-bottom: 1px solid #000000"&gt;Authorized&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" align="center" style="border-bottom: 1px solid #000000"&gt;Completed&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" align="center" colspan="1" style="border-bottom: 1px solid #000000"&gt;Repurchased&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr style="font-size: 8pt" valign="bottom"&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" align="center" colspan="2"&gt;(In millions)&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" align="center" colspan="1"&gt;(In millions)&lt;/td&gt;
    &lt;/tr&gt;
    &lt;!-- End Table Head --&gt;
    &lt;!-- Begin Table Body --&gt;
    &lt;tr valign="bottom" style="background: #cceeff"&gt;
    &lt;td&gt;
    &lt;div style="margin-left:15px; text-indent:-15px"&gt;July&amp;#160;2008
    &lt;/div&gt;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="left"&gt;$&lt;/td&gt;
    &lt;td align="right"&gt;400&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="left" valign="top" nowrap="nowrap"&gt;October 2008&lt;/td&gt;
    &lt;td align="left" valign="top"&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="right" valign="top"&gt;5.9&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr valign="bottom"&gt;
    &lt;td&gt;
    &lt;div style="margin-left:15px; text-indent:-15px"&gt;May&amp;#160;2009
    &lt;/div&gt;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="right"&gt;250&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="left" valign="top"&gt;July 2009&lt;/td&gt;
    &lt;td align="left" valign="top"&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="right" valign="top"&gt;3.7&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr valign="bottom" style="background: #cceeff"&gt;
    &lt;td&gt;
    &lt;div style="margin-left:15px; text-indent:-15px"&gt;July&amp;#160;2009
    &lt;/div&gt;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="right"&gt;750&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="left" valign="top" nowrap="nowrap"&gt;January 2010&lt;/td&gt;
    &lt;td align="left" valign="top"&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="right" valign="top"&gt;9.7&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr valign="bottom"&gt;
    &lt;td&gt;
    &lt;div style="margin-left:15px; text-indent:-15px"&gt;February&amp;#160;2010
    &lt;/div&gt;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="right"&gt;250&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="left" valign="top"&gt;May 2010&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="right" valign="top"&gt;3.3&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr valign="bottom" style="background: #cceeff"&gt;
    &lt;td&gt;
    &lt;div style="margin-left:15px; text-indent:-15px"&gt;August&amp;#160;2010
    &lt;/div&gt;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="right"&gt;1,000&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="left" valign="top"&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="left" valign="top"&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="right" valign="top"&gt;8.3&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr style="font-size: 1px"&gt;
    &lt;td&gt;
    &lt;div style="margin-left:15px; text-indent:-15px"&gt;&amp;#160;
    &lt;/div&gt;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" colspan="2" align="right" style="border-top: 1px solid #000000"&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="left" valign="top"&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" colspan="1" align="right" valign="top" style="border-top: 1px solid #000000"&gt;&amp;#160;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr valign="bottom"&gt;
    &lt;td&gt;
    &lt;div style="margin-left:30px; text-indent:-15px"&gt;Total
    &lt;/div&gt;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="left"&gt;$&lt;/td&gt;
    &lt;td align="right"&gt;2,650&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="left" valign="top"&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="left" valign="top"&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="right" valign="top"&gt;30.9&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr style="font-size: 1px"&gt;
    &lt;td&gt;
    &lt;div style="margin-left:15px; text-indent:-15px"&gt;&amp;#160;
    &lt;/div&gt;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" colspan="2" align="right" style="border-top: 3px double #000000"&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="left" valign="top"&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" colspan="1" align="right" valign="top" style="border-top: 3px double #000000"&gt;&amp;#160;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;!-- End Table Body --&gt;
    &lt;/table&gt;
    &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;
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