I'm going to leave out lwp, and dbi and other overly well knowns and CORE:: moduels assume a basic novice level perl programmer:

Got to haves:

Moose

MooseX::Traits

YAML

XXX

Devel::SimpleTrace

Module::Install

Module::Starter

Extraction:

Text::CSV (the new and improved, for all ___ deliminited files)

DataExtract::FixedWidth (I created it, but it is still probably one of my most used modules)

HTML::TreeBuilder

Content Creation:

Catalyst

Template

I'm probably missing a bunch...

Some of the modules others have suggested legitimately bad imho, like Data::Dumper which has no upside when compaired to XXX. I also regret learning functional-module style perl, i.e. Exporter, vars, libs. et al. Moose ftw. I also regret learning every ORM I've ever learned: they all seem to ultimately be a waste of time.