Games because they were hard and annoying in someway.
Bayou Billy NES - I tried playing this game again several times and wonder how I even made it past stage 2 or 3, not to mention beating the game period.
Double Dragon 3 NES - It was down to me with 3 life bars on the final boss. Way too many bosses on the last stage. Only beat it two player with a friend back in 92.
Friday the 13th NES - Back then even though the game sucks, I just didn't know better and beat Jason several times to get the real unsatisfying ending. Never again.
TMNT NES - I beat it back in 92 at a friends house. It is a hard game until you really get the hang of it, but it still just seems like a pain to want to figure out and beat again.
Ghouls n Ghosts Arcade (Capcom Classics for PS2) and Super GnG SNES - I really don't need to say why.
Art of Fighting 2 Neo Geo (CD version) - Actually did it twice the first month I owned it. Now, this is beating it without loosing a fight so you can get to Geese Howard. Duuuuude, you have no idea what hell it is if you haven't played it. Now when I beat my AES version I shamelessly cheat with the Unibios.
Air Zonk TG16 - Jesus Christ that last stage and the final boss was torturing.
Contra Shattered Soldier PS2 - I actually got 100% ranking and beat the real final boss with the best ending. Man, it took a lot of dying and starting over to do this. You can't miss one non re-spawning enemy or die, I think.
I am sure there are some more, but I can't remember everything. Most of these I beat during the times they were out plus 2 years or so, except Air Zonk about 1/2 a year ago and AOF2 in 98.
Still, I try to beat some games I haven't before and can't imagine doing it again once I do. Most of these are space shooters, a few RPGs, punishing adventure games and most games on the NES.