From that I moved to the SNES, for which I still have a lot of games. I've got most of the roms for those on my mobile phone, and it's quite funny to see the look on people's faces when they hear the Super Mario theme and see what's on my screen
On the PC, I enjoyed Doom, Blood and the likes, going on to "matchbox" racing with NFS Porsche, and pretty much keeping it on through to the 2009 Wolfenstein installment (which was a bit of a disappointment in my book). After this I pretty much moved full-time to Linux, and to less involved independent games like World of Goo and Hedgewars
The online bandwagon isn't all that alluring to me, except a few small MMORPGs from the old days, like MU online, I haven't really found too much fun in it.
When it comes to genres, RTS is the king of the hill for me. Then come RPGs, especially those from the Elder Scrolls series and Neverwinter Nights. I'm not too shabby at shooters either, and I'm more of a Unreal Tournament persona rather than a Quake fan, although I play both of them as well :D