Vagrant boxes, linux servers, and SSH session terminals, oh my! To clean up the mess, I installed mRemoteNG, to put the PuTTY sessions in tabs. Still get to keep my custom settings... just have it all boxed up for neatness now. Recommended.Note that there are a lot of alternatives, and I just don't have time to try them. A quick trip through Wikipedia has an article on programs, and I see a lot of people using SuperPuTTY.
I'll also have to check out KiTTY on some rainy day, but really I have no complaints with PuTTY at the moment. Should I care about KiTTY if I already have PuTTY working nice?