I do NOT suggest Civ IV unless your looking for a major time sink... It's a great game, and isn't hard to figure out at all (unless you really dig into the micromanaging), it just takes forever to complete a game against more than two AIs.
The Sims 2 is a really great game. It's easy to get wrapped up in, but is a lot of fun.
You may wanna try Mass Effect, though I'm not sure if it would run properly on your hardware. It is, hands down, the single greatest game I have ever played. In fact, the night I got it, I stayed up until 7 AM playing it... I didn't even sleep. I just couldn't tear myself away.
World of Warcraft is fun and would run great on your laptop, but I warn you now: this game will chew through your self-control and reduce you into a humanoid blob of addiction. Play at your own risk.
I know it doesn't fit your description very well at all, but I must mention Dawn of War. For a long time this was all I had to do, and next to Mass Effect is the best thing since sliced bread. It's what got me infatuated with PC gaming and RTS games in one blow.
And Peggle is fun, even if it is casual. I doubt PatMan meant any offense. Peggle Extreme is better, though. So much so, in fact, that the unicorn is having its face eaten by a crab. How could it get better?