I purchased an ASUS VG236H in December 2011, and I have enjoyed it ever since the first minute I powered it on, adjusted my refresh rate and moved my mouse cursor around in awe of how smoothly it moved across the screen. Even if you can't maintain 120 FPS in games, the 1-2ms gray to gray response time of the panels is much nicer than the average 5ms panels you get in monitors around the $100 mark. Screen tearing is also much less noticeable if you play without VSYNC enabled and your frame rate exceeds the refresh rate from what I've seen.
If your computer is horrendous though, you're probably better off upgrading it first. A $300 monitor won't improve a $300 PC you got at Walmart 5 years ago.