I seem to find that the modules that I use the most are (in particular order) strict, warnings, Data::Dumper, Log::Log4perl & Test::More.

The first 2 are, IMO, essential in as much as they let perl do even more of the work to help write half-decent code with fewer gotchas.
Log::Log4perl allows me to flexibly instrument the code and Test::More, I use for writing unit tests in a, quite frequently vain, attempt to show that my code does what it should do.
Finally, Data::Dumper supports my, admittedly archaic, code debugging as required when the code is observed (by Test::More test case failures) to be implementing NWITIAF (Not What I Thought I Asked For) behaviour(s).