None influenced me, as they weren't around until I was about 17-18. I do howver play heaps, things like Buffy (Chaos Bleeds), Ratchet & Clank, Burnout series etc.
The one I've been playing most, as you can tell by my posts in some threads, is Canis Canem Edit, or Bully. I have the PS/2 version, and don't really need the Scholarship Edition (doesn't exist for PS/2 anyway so ha) but I'm having shitloads of fun with this one. You can even have lots of fun once you complete all 100% of the game, just by mucking around in freeplay.