I've given up on a lot of games, but usually with the intention of coming back someday. The only games I've actually given up on with no intention of playing again, were FFXII and XIII.

I liked the battle system and characters of 12 enough that I wanted to play, but it just took too damn long to get from place to place. With too many enemies. I stopped, I tried a new playthough, then I stopped again with no intention of playing anymore.

I played XIII up till I thin really close to the end. I'm pretty sure I was, at most, within three hours from the end (mild spoilers a couple of hours after Gran Pulse), but then I realized I just didn't care enough about what happens to waste another second. I'd been playing for twenty hours after I got bored just for the sake of getting to the end, and I just had to cut my loss.

Nah, it's not that hard.  It's fast, but it's the same pattern over and over again and you can take as many hits as he can.  Definitely going to take a few lives, but by the fifth or sixth try at the latest it should be doable.

Because the game was shit and didn't work.

For me it was the PC version of the first Witcher game. After about the first hour of playing it, I was bored with the game. Not only that, but there was no way to turn on vsync in the game, meaning that I would have to deal with screen tearing.

Xenoblade Chronicles. There comes to the point where a game feels too open, large, and long...

Also I was trying to complete FE:PoR, but halfway through I got too tired dealing with archaic layout and design, so I just never found the motivation to keep on playing. Maybe one day though...

Bloodborne.
I see no point in extremely hard games.
There's a point where it stops being fun and just becomes tedious.

I really liked the idea that while you are playing, other people are there too doing their thing yet for some reason they shoved in the idea of making friends and joining people to do things. The grind was a joke and I never did a raid as I never had enough friends to do it and didn't want to join randoms. I gave up for those reasons.

I gave up on Star Ocean 4 as the voice acting hurt my hearing. There are probably others but generally I try to finish games.

Well as a Kid I gave up on multiple games, one was certainly Medievil 2, not much after the Dragon Skeleton Boss Battle at the beginning of the game I kept getting stuck, 4/5 years later I re-played the game and didn't even find the place where I got stuck and ended the game in something like a week...

Five years ago I started Demon's Souls and found it so difficult that, after 6 hours wandering around the very first level without being able to reach the boss (Dying over and over again, losing all my souls and having to go through the whole level again since there were no intermediate bonfires in the first game of the series), I quit in rage cursing it for being a mess with horrible graphics and physics. Last month I gave it another chance and had a blast playing through it. Such a blast that, after finishing it, I had to inmediately start Dark Souls (another incredible game) and DSII after that one (I just killed the Old Dragonslayer). So I could have said Demon's Souls, but I don't know why it became so much "affordable" when I gave it a second chance. What you did (traversing such a long distance without using a bonfire) was crazy =P

The only game I remember giving up is Battletoads. I couldn't get pass the part in which you have to go down to disable a bomb before a super fast rat gets to it =P

Any Bethesda game.