return $fib3_cache{$n} ||= do {

I'd strongly recommend trading //= for ||=. Any function that can return 0, but costs to determine that, looses out as is.

You can get greater benefits still for functions that take low integers as inputs by using an array instead of a hash for the cache:

my @fib4_cache;
sub fib4 {
    my $n = shift;
    return $fib4_cache[$n] //= do {
        $n < 2 ? $n : fib4($n-1) + fib4($n-2)
    };
}
__END__
C:\test>memofib.pl
          Rate     fib1     fib2     fib3     fib4
fib1    88.7/s       --    -100%    -100%    -100%
fib2  219835/s  247838%       --     -89%     -91%
fib3 2073455/s 2338415%     843%       --     -19%
fib4 2551114/s 2877136%    1060%      23%       --
[download]

And see the benefits more clearly if you do away with some of the benchmark overheads by loosing the sub wrappers (The module adds its own wrapper internally):

cmpthese(-1, {
    fib1 => q{ fib1 20 },
    fib2 => q{ fib2 20 },
    fib3 => q{ fib3 20 },
    fib4 => q{ fib4 20 },
});


__END__
C:\test>memofib.pl
          Rate     fib1     fib2     fib3     fib4
fib1    87.4/s       --    -100%    -100%    -100%
fib2  223254/s  255377%       --     -89%     -91%
fib3 2071504/s 2370384%     828%       --     -20%
fib4 2579867/s 2952119%    1056%      25%       --
[download]

And finally, there's a couple more % to be had:

my @fib5_cache;
sub fib5 {
    my $n = shift;
    return $fib5_cache[ $n ] //= do {
        $n < 2 ? $n
        : ( $fib5_cache[ $n-1 ] //= fib5($n-1) )
        + ( $fib5_cache[ $n-2 ] //= fib5($n-2) ) ## corrected; thanks 
+to moriitz
    };
}

__END__
C:\test>memofib.pl
          Rate     fib1     fib2     fib3     fib4     fib5
fib1    89.0/s       --    -100%    -100%    -100%    -100%
fib2  218452/s  245352%       --     -89%     -91%     -91%
fib3 2022174/s 2272005%     826%       --     -18%     -20%
fib4 2478824/s 2785096%    1035%      23%       --      -2%
fib5 2537045/s 2850512%    1061%      25%       2%       --
[download]