I use a notebook and it works great! Just be sure you get a nice GeForce Go Mobile card like the 8600GT that I have. I would order from a company like Dell that allows you to "build your own," that way you can design it for gaming. I got their cheapest model that allowed me to use the 8600GT and I elected to stick with XP since it was going to be a gaming machine. I don't think they offer XP anymore, but I think Vista is finally nearing getting the kinks worked out in terms of gaming. Just make sure you get plenty of RAM. My proc is a 1.66Ghz Core 2 Duo, which is roughly equivalent to a 3Ghz single core, gaming-wise. If I could do anything different though, I'd probably get a much faster proc. Since you'll probably get Vista with it, I'd also get about 4GB RAM (but NOT from Dell, etc. Get it from Newegg or somewhere cheap).
Since you're posting on this site, I'm assuming that you like games that aren't necessarily graphics intensive. I could never run Crysis on my lappy, but I don't want to. It runs every TBS game that I play great, and that's all I care about. Valve games, of course, all run fantastic. The only way to play next-gen games on a laptop is to drop between 2-4 grand on one. I got mine for under $800 and it suits all my needs well. Make sure you Google a bit and look for online coupons; they're usually plentiful and can allow you to get a better setup for cheaper.
I've only had one problem gaming on my laptop: King's Bounty with settings maxed (noAA, 4xAF) was overheating and shutting me down. But, I bought a laptop cooler and haven't had a problem since. I'd recommend a cooler, since gaming creates quite a bit of heat and laptops are so compact.
One minor caveat: laptops are not designed for gaming (unless it's an XPS, Alienware, etc.) so some games may not work right. So far, I haven't found any problems though. I've played Bioshock, Rome:TW, Medieval II:TW, GalCiv2, Oblivion, King's Bounty, HOMM5, and others all on high settings. I hope this helps. Feel free to PM me if you have any more questions.