360- CoD5 beta (I'm weening off this). CoD4. Halo 3. Portal: Still Alive. Braid. Fallout 3 and Gears 2 will be the next ones I go to.
PC- Call me old school, but I still can't get enough of Civ IV. I'd still be playing Civ II if they ended the series.
CivIV - did you get the expansion packs? I love CivIV but haven't gotten the 2 expansion packs yet...I know i'd get started w/ a game and just play it all weekend. I love Civ - been playing since the first one. Civ II I like the least but still like it quite a bit, especially the WW2 scenario.
I keep asking for people to join me in some civ IV but I never get any takers...recently I have been playing Civ IV way too much...it was out of hand. I had to step away for a bit. I am sure I'd jump right back in the saddle though if someone wanted to play.
I've actually never played it online. 
It is pretty slow, but you usually can bang through the first 100-200 turns in a few hours and before a human player the first person goes to war. Once that happens, turns are every 3-4 minutes which seems forever while you stare and wait.
There are options though, you can use something called 'pitboss'...It allows you to host a game somewhere and then persons can log into it and take their turn whenever they want. They even have websites that will email you when everyone has taken their turn. This is really for much larger games though (4+) and makes the game take forever since you actually have to load civ 4, run your turn and turn it off every day.

I have played the game with 4+ persons and 4 cpu a number of times and invertiblely someone quits or sabbatoges the game since they got pinched early. LOL In a regular lan setting it sucks if you take someone out because most of the time that leaves them with nothing to do for 6-10 hours until you complete the game.
You can also set timelimits on each turn but that really sucks most of the time and leads to big time mistakes, especially with noobs.

We also turn off tech trading for a little twist.