FPSs are not lame. They are the backbone of the gaming industry and the starting point for everything we have now (think Wolfenstein/Doom/Doom 2, etc.). That said I play a lot of FPS games, looking forward to COD Ghosts. The COD titles have been some of my favorites. But mostly I play online MMP FPS games. Largely this was kicked off and popularized with Quake Arena, which was great, and currently I play a lot of Combat Arms (free to play korean FPS online, pretty decent engine, good graphics, nothing ground-breaking but playable and fun). I played Civ, and then migrated to Evony, in which I built some alliances and completely took over a few servers, until botting/scripting started ruining the game. I play some Starcraft/Diablo but those types of games never really did it for me. Neither have the GTA titles. They always seemed boring and pointless. And adding sex scenes and torture porn does little if anything to improve them.
Lately I just have almost no time so I, like GF, prefer a game I can jump in and out of quickly, kill a half hour here and there without giant time commitments, and leave alone for long stretches and come back to with nothing really changing, so not playing many persistent games (RPG/RTS etc.), because if I can't get online for a week at a time I don't want my world to be decayed to nothing when I get back to it.
I have also been trying some steam titles. Some of them are fun decently priced, fairly simple to figure out, then fun to come back to again and again. But a lot of them are derivative, can be very glitchy and boring. Kind of a crap shoot. If you go that route definitely get into the forums to try to weed out the crap.
League of Legends consumed my life for a while, but I broke the addiction. And I got a killer machine out of it as I built my comp for the frame rate and game play.
GF check out Combat Arms if you have a good internet connection and decent comp. Don't need anything extravagant but a 3 year old vid card might be taxed a little to give smooth game-play. It's fun and easy to get into.