I use a Gateway NV53A with a 64-bit Windows 7 OS, which is a bit outdated. I picked it up for somewhere in the $450-550 range around a year ago. I'm having trouble remembering.
Here are it's specs:
AMD Pehnom II N830 Triple-Core Processor (2.10 GHz)
4 GB RAM (3.74 accessible)*
ATI Mobility Radeon HD 4250
450 GB HDD
*I believe the RAM is DDR3, but I'm not sure
Technically speaking, this machine should be able to run some new games on minimum graphics settings; the graphics card is the part that would be preventative. The newest game I ever run on this laptop is Left 4 Dead 2, which I can run on max settings if I'm not bogging my computer down with superfluous background processes.
If you got a machine with similar specs and a better graphics card (which I would recommend if you plan on the machine being your primary game station), you should be able to get something passable.
Edit: This model with slight depreciations (dual instead of tri core, for example) is now available for $430 from the retailer, and probably cheaper from any stores that haven't managed to sell their stock of them. I'd guess getting a model with comparable/slightly better specs and a dedicated mid-range graphics card would land you around $650-$750.
Part of the problem getting a machine that runs games in a laptop is that they naturally bump up all the specs in the factory-floor machines as well, which add to the price significantly more than just the additional graphics capability would. I would recommend looking for a mid-range model and seeing if the graphics card is upgradeable, which would give you what you need
for less cost. Also bear in mind that you'll need to pay for any warranty you want (optional) and antivirus as well, which adds to the price a little.
Another option worth considering is getting a cheap netbook for use in class or writing papers, and putting the rest of the money towards buying components to build a good desktop for your dorm. I have a dedicated desktop with much better specs that I built for video editing and gaming. The nice thing about this option is that you can always upgrade your desktop if it becomes obsolete halfway through college, but if your laptop runs out of steam you have less wiggle room.