Part of the value of this thread is that one comes across modules one wouldn't otherwise have checked out. But I'm afraid I'm a meat-and-potatoes kinda guy, and my favourite list is very MOR. But none the worse for that. As Braque says, "all the ancient wisdoms were young once".
jbr::Carp - this is CGI::Carp but with a tiny tweak (replace line 285 print STDOUT "<!-- warning: $msg --> \n" with print STDOUT "warning: $msg <BR>\n") to put warnings in the browser rather than in comments - just the way I like to debug
Exporter - I confess I don't know totally what this does, but I use it whenever I write a module of my own, so I suppose it must be one of my favourites
Time::Local which I partly like because I think the name is quite witty (localtime converts from integer to date... so to go the other way...)
Font::AFM - I only ever used this once, but it gave me a real kick, as I can be quite obsessive about the mere appearance of words on the page, and this is a userful tool for perfecting the layout of generated (and hence unpredictable) text