﻿<?xml version="1.0" encoding="utf-8"?>
<InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema">
  <Version>2.2.0.7</Version>
  <hasSegments>false</hasSegments>
  <ReportName>Capital Stock and Stock Compensation</ReportName>
  <ReportLongName>11001 - Disclosure - Capital Stock and Stock Compensation</ReportLongName>
  <DisplayLabelColumn>true</DisplayLabelColumn>
  <ShowElementNames>false</ShowElementNames>
  <RoundingOption />
  <HasEmbeddedReports>false</HasEmbeddedReports>
  <Columns>
    <Column>
      <LabelColumn>false</LabelColumn>
      <Id>1</Id>
      <Labels>
        <Label Id="1" Label="6 Months Ended" />
        <Label Id="2" Label="Jun. 30, 2010" />
      </Labels>
      <CurrencyCode>USD</CurrencyCode>
      <FootnoteIndexer />
      <hasSegments>false</hasSegments>
      <hasScenarios>false</hasScenarios>
      <Segments />
      <Scenarios />
      <Units>
        <Unit>
          <UnitID>Unit12</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>Unit13</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>
        </Unit>
        <Unit>
          <UnitID>Unit1</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
      </Units>
      <CurrencySymbol>$</CurrencySymbol>
    </Column>
  </Columns>
  <Rows>
    <Row>
      <Id>5</Id>
      <Label>Capital Stock and Stock Compensation</Label>
      <Level>3</Level>
      <ElementName>osg_CapitalStockAndStockCompensationTextBlock</ElementName>
      <ElementPrefix>osg</ElementPrefix>
      <IsBaseElement>false</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ShortDefinition>Capital Stock and Stock Compensation [Text Block].</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>false</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole>terselabel</PreferredLabelRole>
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText>&lt;div&gt;
&lt;div style="text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;" align="left"&gt;&lt;font style="display: inline; font-family: Times New Roman; font-size: 10pt;" class="_mt"&gt;Note J &amp;#8212; Capital Stock and Stock Compensation:&lt;/font&gt;&lt;/div&gt;
&lt;div style="text-indent: 0pt; display: block;"&gt;&lt;br /&gt;&lt;/div&gt;
&lt;div style="text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;" align="left"&gt;&lt;font style="display: inline; font-family: Times New Roman; font-size: 10pt;" class="_mt"&gt;In June 2008, the Company's Board of Directors authorized the repurchase of up to $250,000,000 of the Company's common stock from time-to-time. Such purchases of the Company's common stock will be made at the Company's discretion and take into account such factors as price and prevailing market conditions. As of June 30, 2010, the Company had repurchased 3,798,200 shares of its common stock under the 2008 program (all prior to December 31, 2008).&lt;/font&gt;&lt;/div&gt;
&lt;div style="text-indent: 0pt; display: block;"&gt;&lt;br /&gt;&lt;/div&gt;
&lt;div style="text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;" align="left"&gt;&lt;font style="display: inline; font-family: Times New Roman; font-size: 10pt;" class="_mt"&gt;In the first six months of 2010, the Company awarded a total of 71,008 shares of restricted common stock at no cost to certain of its employees, including senior officers. Restrictions limit the sale or transfer of shares of restricted common stock until they vest, which occurs over a four or five-year period. During the restriction period, the shares will have voting rights and cash dividends will be paid if declared. The weighted average fair value of the restricted stock issued during the six months ended June 30, 2010 was $43.40 per share (the market price at date of grant). In addition, in the first six months of 2010, options covering 141,998 shares were granted at the market price at the date of the grant. Such options were valued using the Black-Scholes option pricing model and expire ten years from the grant date. The exercise price of options granted during the six months ended June 30, 2010 was $43.40 per share (the market price at date of grant). The grant date fair value of options granted during the six months ended June 30, 2010 was $13.53 per share.&lt;/font&gt;&lt;/div&gt;
&lt;div style="text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;" align="left"&gt;&lt;font size="2" class="_mt"&gt; &lt;/font&gt;&amp;nbsp;&lt;/div&gt;
&lt;div style="text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;" align="left"&gt;
&lt;div&gt;
&lt;div style="text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;" align="left"&gt;&lt;font style="display: inline; font-family: Times New Roman; font-size: 10pt;" class="_mt"&gt;In the first six months of 2010, the Company granted a total of 44,142 performance related restricted stock units to covered employees. The Company did not make any performance related restricted stock unit awards during the first six months of 2009. Each performance unit represents a contingent right to receive shares of common stock, based on a formula, if certain market related performance goals are met and the covered employees are continuously employed through the end of the period over which the performance goals are measured. The performance units have no voting rights and may not be transferred or otherwise disposed of. The covered employees are entitled to dividends in the form of additional performance units at the same time dividends are paid on the Company's common stock in an amount equal to the result obtained by dividing (i) the product of (x) the amount of units owned by the covered employee on the record date for the dividend times (y) the dividend per share by (ii) the closing price of a share of the Company's common stock on the payment date. The performance units resulting from the reinvested dividends will convert into shares of common stock, using the formula contained in the original grant and will vest at the end of the performance period. At the date of grant of the performance related restricted stock awards, the fair market value of the Company's stock was $43.40 per share. The estimated weighted average grant-date fair value of the performance related restricted stock awards in the first six months of 2010 was $52.43 per share.&lt;/font&gt;&lt;/div&gt;
&lt;div style="text-indent: 0pt; display: block;"&gt;&lt;br /&gt;&lt;/div&gt;
&lt;div style="text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;" align="left"&gt;&lt;font style="display: inline; font-family: Times New Roman; font-size: 10pt;" class="_mt"&gt;In the first six months of 2010 and 2009, the Company granted a total of 30,444 and 33,840 restricted stock units to its non-employee directors, respectively. Each restricted stock unit represents a contingent right to receive one share of common stock upon the non-executive director's termination of service as a board member. Such restricted stock units vest ratably over a four-year period, which period may be accelerated provided that the director has served until the earlier of (a) the first anniversary of the grant date or (b) the next annual meeting of the Company's stockholders. The restricted stock units have no voting rights and may not be transferred or otherwise disposed of while the non-employee director is a director. The non-employee director is entitled to dividends in the form of additional restricted stock &lt;/font&gt;&lt;font style="display: inline; font-family: Times New Roman; font-size: 10pt;" class="_mt"&gt;units at the same time dividends are paid on the Company's common stock in an amount equal to the result obtained by dividing (i) the product of (x) the amount of units owned by the non-employee director on the record date for the dividend times (y) the dividend per share by (ii) the closing price of a share of the Company's common stock on the payment date, which restricted units vest immediately on the payment date for the dividend. At the date of the awards in the first six months of 2010 and 2009, the fair market value of the Company's stock was $39.41 and $35.46 per share, respectively.&lt;/font&gt;&lt;/div&gt;
&lt;div style="text-indent: 0pt; display: block;"&gt;&lt;br /&gt;&lt;/div&gt;
&lt;div style="text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;" align="left"&gt;&lt;font style="display: inline; font-family: Times New Roman; font-size: 10pt;" class="_mt"&gt;Compensation expense is recognized over the vesting period, contingent or otherwise, applicable to each grant, using the straight-line method.&lt;/font&gt;&lt;/div&gt;&lt;br /&gt;&lt;/div&gt;&lt;/div&gt; &lt;/div&gt;</NonNumbericText>
          <NonNumericTextHeader>Note J &amp;#8212; Capital Stock and Stock Compensation:

In June 2008, the Company's Board of Directors authorized the repurchase of up to $250,000,000 of the</NonNumericTextHeader>
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDataType>us-types:textBlockItemType</ElementDataType>
      <SimpleDataType>textblock</SimpleDataType>
      <ElementDefenition>Capital Stock and Stock Compensation [Text Block].</ElementDefenition>
      <ElementReferences>No authoritative reference available.</ElementReferences>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
  </Rows>
  <Footnotes />
  <NumberOfCols>1</NumberOfCols>
  <NumberOfRows>1</NumberOfRows>
  <HasScenarios>false</HasScenarios>
  <MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel>
  <SharesRoundingLevel>UnKnown</SharesRoundingLevel>
  <PerShareRoundingLevel>UnKnown</PerShareRoundingLevel>
  <HasPureData>false</HasPureData>
  <SharesShouldBeRounded>true</SharesShouldBeRounded>
</InstanceReport>
