There have been a lot, but some of the main ones are:

FF VII: Got to the save spot right before Sephiroth and just quit playing. I'd go back and finish it if my PS2 still worked.

FF VIII: Played the game to the last disc, but couldn't beat the boss that started at the very beginning of it. I had no way to level up or get items so I quit.

FF XII: Just lost interest. I think I have a problem beating FFs.

Bioshock: Near the end I had to get a key for some locked door. I didn't feel like finding the key so I quit playing and never went back.

So many games I haven't beaten:

Jet Force Gemini (damn spaceship parts)
Turok (no 64 memory card)
Metal Gear Solid for GBC (just got stuck at one point. I'll probably never figure out where to go)
Lord of the Rings: The Return of the King (crap compared to the Two Towers)
Dark Cloud
Metroid Prime (just couldn't get into it)
REmake
Super Mario Galaxy
No More Heroes (and probably never will)
Folklore (just got it, so I have an excuse)

metal gear solid 2 substance. i really hate raiden.

 Konami of America really picked a bad VA for Raiden.  He sounded like a man in the Japanese version.  Actually, he sounded like a total hardass.

I've been pretty lazy lately, I haven't beaten Paper Mario, or Twilight Princess.....I feel fairly ashamed.

Well, let's see. PC GRAW (I'm trying to beat it dammit, it's so friggin hard) Devil May Cry, Zack and Wiki, Final Fantasy X, Xenosaga, Star Ocean 3, Zelda: Wind Waker, Final Fantasy XII, Viewtiful Joe, Metroid Prime, Soul Calibur II?

SUPER MARIO GALAXY!!!!

I Know but i cant get past dreadnought purple coins! argh it kills me!!!

oh and I haven't beaten Pokemon Pearl and FFXII: RW on my DS, though I'm currently going through FFCC, so I'll probably get back to those other two later.

Some Games I've started but not finished:
Gladius
Fire Emblem Gamecube
Fire Emblem Gameboy Advance
Battallion Wars
Super Paper Mario
Beyond Good and Evil
Final Fantasy Crystal Chronicles
Prince of Persia Warrior Within
Baten Kaitos Origins
Summoner Goddess Reborn
Sphinx and the Cursed Mummy
Phantasy Star Online 1 and 2
X-men Legends
Zack and Wiki

Well this is a funny thread, you post that you haven't beaten my favorite game and I post and say I haven't beaten your favorite game.

However, it's not that I wasn't interested in Okami, just didn't get enough time! I'm gonna try and play it tomorrow.

And Okami is by no means the only game I haven't finished, I have like hundreds....ALttP, Super Metroid, SMB3, Shadow of the Colossus (haven't even started it yet!) are only a few...

As for me, I've been kind of busy and have been suffering from a cold for the past week or so, so that's why I haven't posted for a while.