I would suggest to shoot for something with 1600x900 or 1920x1080 display if you can afford it - really improved experience for gaming.
However, if you don't mind gaming at 1366x768 or 1280x720, there are quite a few laptops in the $500-600+ range that will run most games just fine at that resolution.
If you want to run games at 1080p, you will likely be looking at something least around $800-900 or more, any laptop with 6770m, 5830/5850m, 7690m, 550m, 555m, 640m, or better DX11 graphics cards will be able to run most games at 1080p. (Not going to run Crysis / Metro2033 at that resolution, but 99% of games)
At 900p, you can find laptops that are a bit cheaper, with weaker GPUs a step down from the ones above, sometimes priced as low as the $600 range or so, depending on the details.
All of the above, however, only describes the current generation of laptops with Sandy Bridge CPUs and 40nm mobile graphics cards.
Just this week Ivy Bridge and 28nm AMD and NVIDIA mobile graphics cards have been announced. In the next few weeks and coming months, you will be able to find cheaper laptops that run games better at 1600x900 and 1920x1080.