There is a simple polygon area computation that comes out negative if the polygon is clockwise and positive if it is counterclockwise. Here is some perl code that computed it for a polygon object I wrote (not included).

sub GreenTheoremTest {
   my ($poly) = @_;
   my $n = $poly->getSize;
   my $i;
   my $asum = 0.0;
   for ($i = 0; $i < $n; $i++) {
      my $i1 = ($i + 1) % $n;
      my $x = $poly->getPoint($i)->x;
      my $y = $poly->getPoint($i)->y;
      my $x1 = $poly->getPoint($i1)->x;
      my $y1 = $poly->getPoint($i1)->y;
      $asum += $x*$y1 - $x1*$y;
   }
   return $asum;
}
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Update2: My assertion that it will work for self-crossing polygons is refuted by counterexample here.

Update:It will work even for concave and self-crossing polygons. But because the test does not work for colinear points and other zero-area polygons, I use it like this:

my $EPSILON = 1e-20;
my $asum = GreenTheoremTest($poly);
if (abs($asum) < $EPSILON) {
   print "Polygon area is too small to be sure of direction!\n";
} elsif ($asum < 0.0) {
   print "Polygon is clockwise\n";
} else {
   print "Polygon is counterclockwise\n";
}
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