Here's a typical day for me. I get up. I log into my home RT queue to see if there's any personal stuff I need to do today - bills to pay, stuff I need to take to work, etc. It's OK, because I can get at all the details from work anyway, thanks to my DSL. Head into work. Log into my work's RT system, look at the things I need to do today, deal with tickets coming in from users, and so on.
Get home. Log into CPAN's RT system, handle any bugs in my modules, and fire off responses to people lodging bug requests. All the patches are there in RT, so I can just copy and paste them into patch and I've got a release. Check that into Perforce and we're good to go. I don't need to make much of a Changes file, since I can just point everyone at the tickets.
Log into perl.org's RT system and check out the status of Parrot. Ideally, I'll have all the outstanding Parrot patches in there too.
Next, I log back into my own RT system and check the Perl queue, which has all the neato-keen Perl things I've thought of and not got around to implementing. Stare at them. Fail to get around to implementing them. Play quake and/or Go instead.
RT: It doesn't make you more productive, but it certainly makes you more organized.