This might not be as slick as the lookahead approaches described above, but in the spirit of TMTOWTDI here's a version that uses pos and the @- array, which contains the offset of the start of the last match (see perlvar for more info):

sub count_matches
{
    my ( $pattern, $string ) = @_;
    my $num_matches = 0;

    while( $string =~ m/$pattern/gi )
    {
        pos( $string ) = $-[0] + 1;
        $num_matches++
    }

    return $num_matches;
}
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Update: For monks (like me) that didn't understand why a pattern consisting entirely of a zero-width lookahead assertion (m/(?=AA)/g, see the above responses) doesn't get stuck in an infinite loop, see perlre, "Repeated patterns matching zero-length substring". From that doc:

Perl allows such constructs, by forcefully breaking the infinite loop ... when Perl detects that a repeated expression matched a zero-length substring.

To break the loop, the following match after a zero-length match is prohibited to have a length of zero.

... the second best match is chosen if the best match is of zero length ... the second-best match is the match at the position one notch further in the string.