One way you can speed up matching on lots of regular expressions (assuming that matching is infrequent) is to combine them with alternation. This cuts down on the number of matches you need to do. This can improve the speed lots (over 12 times as fast here, with 91 matches in 45424 lines of text):

$ perl multire.pl
Benchmark: running using alternates, using foreach, each for at least 30 CPU seconds...
using alternates: 30 wallclock secs (30.07 usr +  0.09 sys = 30.16 CPU) @  2.69/s (n=81)
using foreach: 30 wallclock secs (30.09 usr +  0.02 sys = 30.11 CPU) @  0.20/s (n=6)
                 s/iter    using foreach using alternates
using foreach      5.02               --             -93%
using alternates  0.372            1248%               --

Here's the code:

#!/usr/bin/perl -w
use strict;
use Benchmark;

#$ wc /usr/share/dict/words
#  45424   45424  409276 /usr/share/dict/words
my $file = '/usr/share/dict/words';

# These callbacks could do whatever you want.
# They have the matching line passed in.
sub foundThe { }
sub foundAeig { }
sub foundCat { }

my %specs = (
    '^the'    => \&foundThe,
    'at[ei]g' => \&foundAeig,
    'cat$'    => \&foundCat,
);

my %cookedSpecs = map { qr{$_}, $specs{$_} } keys(%specs);

sub usingForeach
{
    $count = 0;
    open FILE, $file or die "can't open $file: $!\n";
    while (<FILE>)
    {
        foreach my $pattern ( keys(%cookedSpecs) )
        {
            if (m{$pattern})
            {
                $cookedSpecs{$pattern}->($_);
            }
        }
    }
    close FILE;
}

sub usingAlternates
{
    my $altpattern = join ( '|', map {qr{$_}} keys(%specs) );
    $count = 0;
    open FILE, $file or die "can't open $file: $!\n";

    while (<FILE>)
    {
        if (m{$altpattern})
        {
            foreach my $pattern ( keys(%cookedSpecs) )
            {
                if (m{$pattern})
                {
                    $cookedSpecs{$pattern}->($_);
                }
            }
        }
    }
    close FILE;
}

Benchmark::cmpthese(
    -30,
    {
        'using foreach'    => \&usingForeach,
        'using alternates' => \&usingAlternates
    }
);
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update: clarified callbacks: they don't have to do the same thing.