I prefer to only use recursion when it's absolutely necessary (basically, almost never), so here's my version using a queue:

use strict;
use warnings;

my ($dir, $file, $path);
my ($script) = $0 =~ /:?([^:]+)$/;

my @dirs = ':';
while ($dir = shift(@dirs)) {
    opendir(DIR, $dir);
    while ($file = readdir(DIR)) {
        next if $file eq $script;
        $path = "$dir$file";
        if (-d $path) {
            push (@dirs, "$path:"); next;
        }
        #########
        # Open each $path and process
        #########
    }
}
[download]

This is designed to work on a Mac (see the : directory separators) and also designed to spider whatever directory the script is in (hence no $base definition, and two lines of code making sure the script itself isn't messed with).

Just another viewpoint. This is a regular question, and probably the third time I've posted this to various threads.