For ~$800, you could get a computer where you can't really complain about the quality of any game, even at 1080p. I spent $850 on mine and that's the case.
You won't be able to max out really recent or highly intensive games (the game I haven't been able to max are Crysis, ARMA, STALKER CoP, Metro 2033, Just Cause 2 and GTAIV) but none of them look bad by any stretch of the word.
If you can deal with a few jaggies and maybe not breathtaking but still good effects, you can get a very good machine for ~$800.