Here is my list in no particular order:

• mod_perl
• CGI::Application, thanks Jesse Erlbaum!
• Apache::Session
• HTML::Template, thanks samtregar!
• DBI & Co.
• Apache::DBI
• XML::Simple, thanks grantm!
• CGI::Upload, thanks rob_au!
• Regexp::Common, thanks Abigail-II!
• Storable
• Mail::Sender, thanks Jenda!
• LWP
• HTML::TokeParser
• HTML::TokeParser::Simple, thanks Ovid!
• Image::Magick and GD
• Cache::Cache
• File::Path and File::Copy
• File::MMagic
• Config::General
• XML::RSS
• libapreq
• URI

Modules I would like to know and use:

• Class::DBI
• AxKit, thanks Matts!
• Petal
• XML::LibXML
• Rosetta
• SPOPS, thanks lachoy
• SOAP::Lite

Ciao, Valerio

update: many thanks to all the authors of these modules; please, /msg me with their nicknames at the Monastery if you know them and I'll update the list above.

update2: Thanks to rob_au and Jenda for their help.