mod_perl2 is really difficult to beat if you need to dig into the guts of Apache. DBIx::Class is a huge win if you need/want an ORM but you've been given a really weird pre-existing DB schema. POE has been around forever, and makes really stable long running daemons that don't have to be babied. CPAN has stupid amount of tools for automating sysadmin tasks, all of which you'll probably end up using once, putting in a cronjob somewhere and forgetting about because it will just work. Any time you need to deal with something old, or weird, or both there's probably a CPAN module for that, you can find it via search, and it probably has tests and docs. Template Toolkit for creating uglyass text is both nice to use and full featured (if you don't want to go down the XSLT hole). I've also found that Perl handles I18N, unicode and uglier things (like shift-jis) fairly well. Almost every payment processor has a module, and they all have a standard(ish) API, so they're mostly interchangeable. Likewise crypto stuff is fairly standardized and pretty complete. In general, if you have to tie something to something else that's weird, Perl is a good bet (because someone has probably done it, put it on CPAN, and documented it).

That's a few of the problems I think it stands out as a great tool for.