Go
KGS Go tutorial All tutored up! (I still suck.)
According to BPT, everything I could possibly need to learn go
RISK
http://warfish.net/: play-by-email RISK, with map and rules variants galore. Send SteveKillen an email if you want to join a game!
I'm currently designing a War of the Ring map for warfish using Chris Guerette's excellent PDF map of Middle Earth.
Settlers of Catan
Catan's great. I haven't explored the add-ons yet, though.
Carcassonne
A fast-paced tile placement game.
Bridge
More of an intimation of a hint of an inkling of an urge to to learn to play than any concrete desire yet. Anyone up for it?
Canasta
O Canasta, game of my peoples. (Well, my family, anyway.)