I think this is a reasonable question; the choices of CPAN modules is overwhelming, and yet there are some modules that I use frequently.

use Getopt::Long;  # I use this in all my programs
use Carp qw(cluck confess);
use Time::HiRes;   # I wish this was Perl's default
use Win32;         # When I need to call a Win32 DLL
use XML::LibXML;   # Meets all my XML needs; See also XML::SemanticDif
+f
use LWP;           # LWP & friends for web stuff
use Exporter;      # For writing my own modules
use IO::Handle;

# Some less frequently used favorites
use Term::ANSIColor;  # The world is better in color
use Socket;        # When you need to do your own socket thing
use DateTime::Format::* # For date/time processing
[download]

I hope that helps.