I guess it depends on what kind of domain your working in as to what you consider an "essential" module.

I'm doing lots of web based stuff right now, so an essential module is CGI::Application/HTML::Template. I also find Date::Manip great for doing, interestingly enuff, date stuff.

I too have also rolled my own interface to the DBI, which has become essential to most of the stuff we do in the office.

We also use Digest::MD5. Its got all sorts of applications, however we use it to generate session id's in our web apps.

Prolly one of the most heavily used modules is Data::Dumper, (we mainly use it for debugging), but of course that is core.. :-)