I think I'm pretty good really. I manage to pick up the basics of any given genre pretty quickly, and be a match for the more veteran players after only a bit of practice. I have good hand-eye coordination, fast reflexes and quite a lot of experience with a decent number of genres, making me quite a veteran player to begin with.
For example, Modern Warfare 2 was only my second FPS on the PS3, yet I had no problem starting this game on the more higher difficulties. Or TF2 on the PC, in only a week or 2 I became one of the quickest and overall best sniper on a certain clan server. Then again, I'm naturally good at shooters (either TPS or FPS), so that doesn't count for most other genres.
That said, even though I master the basics of almost any game really fast, it's still very hard for me to become a real master in some genres. For example, I am way too patient to become really good at RTS games (although I used to be a master in Age of Empires 2, through sheer willpower and hours of play, I was a dedicated kid). I am very reluctant to actually attack my enemy, in fear of leaving my base exposed, and I just can't direct a major battle and economical management in my base at once. Maybe a more tactical game like Dawn of War 2 would suit me, although I got my ass kicked so incredibly hard in DoW2's beta. I just plan too much I think, I can't strike quickly enough.
Also rhythm games. Maybe if I practice a lot, but I never managed to play Donkey Konga as well as my little brother could. I have my limits.