Code Golf - π day

C: 131 chars

(Based on the C++ solution by Joey)

main(i,j,c,n){for(scanf("%d",&n),c=0,i|=-n;i<n;puts(""),i+=2)for(j=-n;++j<n;putchar(i*i+j*j<n*n?c++,42:32));printf("%g",2.*c/n/n);}

(Change the i|=-n to i-=n to remove the support of odd number cases. This merely reduces char count to 130.)

As a circle:

      main(i,j,
   c,n){for(scanf(
  "%d",&n),c=0,i=1|
 -n;i<n;puts(""),i+=
 0x2)for(j=-n;++j<n;
 putchar(i*i+j*j<n*n
 ?c++,0x02a:0x020));
  printf("%g",2.*c/
   n/n);3.1415926;
      5358979;}

XSLT 1.0

Just for fun, here's an XSLT version. Not really code-golf material, but it solves the problem in a weird-functional-XSLT-kind of way :)

<?xml version="1.0"?>
<xsl:stylesheet version="1.0"
                xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
                xmlns:msxsl="urn:schemas-microsoft-com:xslt" >
  <xsl:output method="html"/>

  <!-- Skip even lines -->
  <xsl:template match="s[@y mod 2=0]">
    <xsl:variable name="next">
      <!-- Just go to next line.-->
      <s R="{@R}" y="{@y+1}" x="{-@R}" area="{@area}"/>
    </xsl:variable>
    <xsl:apply-templates select="msxsl:node-set($next)"/>
  </xsl:template>

  <!-- End of the line?-->
  <xsl:template match="s[@x &gt; @R]">
    <xsl:variable name="next">
      <!-- Go to next line.-->
      <s R="{@R}" y="{@y+1}" x="{-@R}" area="{@area}"/>
    </xsl:variable><!-- Print LF-->&#10;<xsl:apply-templates 
      select="msxsl:node-set($next)"/>
  </xsl:template>

  <!-- Are we done? -->
  <xsl:template match="s[@y &gt; @R]">
    <!-- Print PI approximation -->
    <xsl:value-of select="2*@area div @R div @R"/>
  </xsl:template>

  <!-- Everything not matched above -->
  <xsl:template match="s">
    <!-- Inside the circle?-->
    <xsl:variable name="inside" select="@x*@x+@y*@y &lt; @R*@R"/>
    <!-- Print "*" or " "-->
    <xsl:choose>
      <xsl:when test="$inside">*</xsl:when>
      <xsl:otherwise>&#160;</xsl:otherwise>
    </xsl:choose>

    <xsl:variable name="next">
      <!-- Add 1 to area if we're inside the circle. Go to next column.-->
      <s R="{@R}" y="{@y}" x="{@x+1}" area="{@area+number($inside)}"/>
    </xsl:variable>
    <xsl:apply-templates select="msxsl:node-set($next)"/>
  </xsl:template>

  <!-- Begin here -->
  <xsl:template match="/R">
    <xsl:variable name="initial">
      <!-- Initial state-->
      <s R="{number()}" y="{-number()}" x="{-number()}" area="0"/>
    </xsl:variable>
    <pre>
      <xsl:apply-templates select="msxsl:node-set($initial)"/>
    </pre>
  </xsl:template>
</xsl:stylesheet>

If you want to test it, save it as pi.xslt and open the following XML file in IE:

<?xml version="1.0"?> 
<?xml-stylesheet href="pi.xslt" type="text/xsl" ?> 
<R> 
  10 
</R> 

Perl, 95 96 99 106 109 110 119 characters:

$t+=$;=1|2*sqrt($r**2-($u-2*$_)**2),say$"x($r-$;/2).'*'x$;for 0..
($u=($r=<>)-1|1);say$t*2/$r**2

(The newline can be removed and is only there to avoid a scrollbar)

Yay! Circle version!

    $t+=$;=
 1|2*sqrt($r**
2-($u-2*$_)**2)
,say$"x($r-$;/2
).'*'x$;for 0..
($u=($r=<>)-1|1
 );$pi=~say$t*
    2/$r**2

For the uninitiated, the long version:

#!/usr/bin/perl

use strict;
use warnings;
use feature 'say';

# Read the radius from STDIN
my $radius = <>;

# Since we're only printing asterisks on lines where y is odd,
# the number of lines to be printed equals the size of the radius,
# or (radius + 1) if the radius is an odd number.
# Note: we're always printing an even number of lines.
my $maxline = ($radius - 1) | 1;

my $surface = 0;

# for ($_ = 0; $_ <= $maxline; $_++), if you wish
for (0 .. $maxline) {
    # First turn 0 ... N-1 into -(N/2) ... N/2 (= Y-coordinates),
    my $y = $maxline - 2*$_;

    # then use Pythagoras to see how many stars we need to print for this line.
    # Bitwise OR "casts" to int; and: 1 | int(2 * x) == 1 + 2 * int(x)
    my $stars = 1 | 2 * sqrt($radius**2-$y**2);
    $surface += $stars;    

    # $" = $LIST_SEPARATOR: default is a space,
    # Print indentation + stars 
    # (newline is printed automatically by say)
    say $" x ($radius - $stars/2) . '*' x $stars;
}

# Approximation of Pi based on surface area of circle:
say $surface*2/$radius**2;

FORTRAN - 101 Chars

$ f95 piday.f95 -o piday && echo 8 | ./piday

READ*,N
DO I=-N,N,2
M=(N*N-I*I)**.5
PRINT*,(' ',J=1,N-M),('*',J=0,M*2)
T=T+2*J
ENDDO
PRINT*,T/N/N
END

    READ*,N
  K=N/2*2;DO&
 I=1-K,N,2;M=&
(N*N-I*I)**.5;;
PRINT*,(' ',J=&
1,N-M),('*',J=&
0,M*2);T=T+2*J;
 ENDDO;PRINT*&
  ,T/N/N;END;
    !PI-DAY