With XP, you can technically run it with 64mb. I have an old K6 Toshiba laptop w/ XP Pro SP2, all updates on it, and 64mb ram. It has NOTHING else on it, and runs VERY slow, but does run. Sadly, it can only be upgraded to 128mb.
XP will run on 128mb alright if you don't run a lot of applications at the same time (that includes virus and e-mail protection programs, as those love to chew up system resources). I'd personally wouldn't run w/ anything less than 256mb.
My g/f as a Dell Laptop, had only 128mb ram, around a 800Mhz Celeron (or there abouts), 8mb video card. She bought Sims 2, and it just wouldn't run on the PC. It would load for 10 minutes, and when it finally did get going, it wasn't even playable. I toss in an extra 256mb ram (384 total), did NOTHING else, and she can actually play and enjoy the game now. Yes, it still runs slow (her processor doesn't meet minimum requirements, and her 8mb video card is way under the minimum requirements), but going from not able to play to being able to play is quite and upgrade.
Simply put, you can never have too much ram. I'll take a 1GHz processor w/ 1gig ram over a 3.4Ghz processor w/ 128Mb ram (all other things being equal).