I'm curious. Which games, for whatever reason, did you never finish? I've lots.
Starlancer: Last level = Hardest Level Ever! I just couldn't do it. Fun though. I recommend to anyone who likes Freespace.
Dungeon Keeper 2: Couldn't concertrate enough near the later levels. Too hard/repititive
Temple of Elemental Evil: I really really want to like this game. It's got great graphics, I love the turn based combat (brings back memories of the Goldbox series), the story was there, but the NPCs are boring, quests evolve to much backtracking, the interface appear to be unfinished ie: Having to manually put a flag on the map so you can remember which building it which. Not having enough information in game about the various feats, and skills. I've played BG2, and NWN enough that I have a idea about alot of them, but not all, and a PDF manual sucks. Maybe I should go dual-monitor. It should have been a fantastic game.
Ultima 9: I liked the freedom of the others ultima (even U8), but this one leads you by the nose ring commonly used to lead bulls.
Giants - Citizen Kabuto: Too hard. Building a base, while hunting foods, hunting Smarties, killing bad guys (takes most of the time) is incredibly aggravating. Still a fantastic game though.
Nox: Did everything but kill Hecubah. Just never around to it
Clive Barkers Undying: Mansion was freaky. Rest got a bit boring.
Thief - The Dark Project: I didn't approve of undead in the game. I only ever got toplay that late at night in the dark. Kinda creepy.
Pools of Darkness (Goldbox 3): I just couldn't do the last fights about the Balor (or Balrog). I beat the dragons. Beat the beholders. Had only one character left to kill the Minions of Bane, and the Balor himself.
Black and White: Micro-management. I try to be a good god, but my theory of "If you worship to the point of starvation you're a bloody idiot." and so i ended up red and veiny. Though my cow was white and glowing ....and fat.
Actually I could probably name just about ever I've ever played :p
Karl

I did finish Nox, Temple of Elemental Evil and Dungeon Keeper 2 (great games all of them). But I could never finish Divine Divinity, I got stuck near the end of the game =(
PS: I felt the same as you about Clive Barker's Undying (mansion was great, rest a little meh)

Prince of Persia: The Warrior Within
All of the boss battles in it were pretty terrible, but the very last one just made me bellow OH F*CK OFF and give up altogether. Which is a shame, because despite the lameness of the game's tone, I was actually really enjoying the story.
And I'm sure there have been others; I remember at the end of last year Eurogamer posted some new year's resolutions for gamers, one of which was basically "just give up." Meaning, when a game is reducing you to a spitting, screaming ball of rage, just walk away with what remains of your dignity. I thought it was good advice. (I've also found that I often walk back at a later date and kick the difficult section's ass)

For me its almost every RPG game. I love them, but rarely do I finish it. I donno why. I think the only rpg I finished was Pools of Radience.

*Insert very long list here*
The one I most regret not finishing though was probably Fallout 1+2....I could never really get into the rhythm of the game.

Prince of Persia - sands of time. There is this obscenely long and difficult puzzle (with no mid-point-resets) near the end of the game, after wasting a whole afternoon on it, I got fed up and uninstalled it.
All the Ultima games except #1 and #4. Try as I might, I just can't get too far with the rest.
ToEE, Giants:CK and DivDIv as others have mentioned for pretty much the same reasons.

I've never finished a game by Blizzard except Diablo 2 (minus the expansion pack) and I've played most of their games. I think I'll also say that Baldur's Gate, Baldur's Gate II, Icewind Dale, and Icewind Dale II I'd always start but I'd always find some kind of snag and try to reroll a better character, never finishing any of those games. Come to think of it I didn't finish Neverwinter Nights either, but I played the multiplayer on that game for oh-so long.
Let's see... there's also...
Temple of Elemental Evil - I tried very hard to get into this game and make the best party possible but I just found the game frustratingly hard. And what's more is that people tell me it's not hard... :(
Tron 2.0 - I liked the story bits and the graphics, but I never took the time to complete it.
Alien vs. Predator 2 (and the expansion) - It gets to a point where it stops being interesting. Most of the starting stories, particular the Alien's stories are fantastic and I still remember them even now, but other than that the game didn't really do much else for me.
Black and White - I stuck on the island before last and kept going back to pick new creatures.
Black and White 2 - I'm not sure why...
Majesty Expansion - Since the difficulty is set depending on the mission it becomes very very difficult to complete.
There's loads more, but that's all I can list at the moment.

black and white (just too repetive on the creature; I had to time to micro manage either the creature or the people; but to succed I had to do both)
Prince of Peria: sands of time (stuck on a puzzle towards the end)
POP: warrior within (just didn't enjoy it)
Condemed Criminal origins (I got it with my X360 along with ES4: Oblivion and that took a lot of my gaming time for months)
I tend to finish most games I start unless either I determine the suck, encounter a bug that prevents completion only on rare occasion do I get stuck to the point that I give up. POP:SOT was the last time that has happened.

NWN - Could just never get into at all.

I find myself intrigued to know what puzzles that a couple of you got stuck on in PoP: SoT as it was a game I breezed through without any trouble. I didn't find any of the puzzles to be that hard and really enjoyed the library level with the mirrors as that took a lot of spatial awareness to work out the solution.
As for games never finished, far too many to list as boredom is the normal cause of me leaving a game to gather dust on the shelf.

Big list here. I just lost the interest in :
Clive Barker's Undying (or was it because a reformat, I don't remember)
Ironstorm (stuck)
Unreal II was boring as hell...
lots of other titles, sadly. And I hope to finish them one day!

battle toads because its impossible. lol

Every single WipEout game ever made. Only robots can finish them!!

Metroid Prime 3: Corruption on Hypermode
Managed to take out first phase of last boss, but got owned by second, got fed up after that
KotOR 2
Game saves got corrupted at penultimate planet, so I uninstalled it
Planescape Torment
Got through the first 10min, but I wasnt paying attention to the story, which was my downfall. Might revisit it soon