Second chance games... The Best.

I hated it, but then I played it again. I liked it... I loved it... I was wrong.
 
Max Payne 2 for me. I loved the first, but the second turned me off, thought it was a bad sequel. I just started to play it again. I was wrong.

Morrowind, possibly more.

I guess the most recent example for me is Final Fantasy V. First time I played it, I got about ten hours into it and didn't like where the story was going at all. I went back to it last year, forced my way through the first third of the game (which was still as painful as the first time), and found the rest of the game was a hell of the lot better. 

Project Sylpheed: I played the demo and couldent understand what I was seeing or how to control the ship. Recently my friend brought over his copy of the game and it clicked and I loved it.

Monster Hunter (Franchise anyways).
 
"What is this? I don't even..."
 
-> 6 Years later
  
"OOOOOOOOOOHHHHHHH! I get it!"

I just ordered SFIV.    I'm really hoping it will fit in this category. 
Hated it when I rented it but I have been playing alot of TEKKEN and well I need another good fighter.

But for now PaRappa the Rapper is easily on the top of my list.

Halo...Once you land on Halo at the beginning and are running around trying to find the other soldiers that bored the shit out of me. Then this summer I tried it again, by the end of summer I had finished Halo 1-3. I'm now a fan.

Borderlands might be that game for me, or Fallout 3... I just haven't given them second chances though.

Banjo Kazooie: Nuts & Bolts for me.  I really didn't hate it a first, just thought it was kinda cool and neat.  Then I picked the game up about a year later and fell in love with it.

Grand Theft Auto 4. Got bored, moved on, came back, finished it. Not the greatest experience, but it was a decent enough game.

Mass Effect - the original 1.0 PC version crashed and bugged out quite a few times for me, and it got so bad that eventually i was just done with it, also i wasn't digging the game that much in all honesty. Then around November i re-installed it, and not only was there a patch to fix the issues, i also fell in love with the universe itself.

Fallout 3: Partially because I was stuck, lost in the DC ruins and partially because I messed the story up starting a mission that was way ahead of where I was. 

Oblivion: I just didn't totally understand the leveling system in the game.  I had a character at about level 7 and never really cared to play on.  Then I tried it again figured it out and put far more hours into it than I should ever have.  
 
I'm sure there are many others, but that is all I can think of for the current gen systems.

" Halo...Once you land on Halo at the beginning and are running around trying to find the other soldiers that bored the shit out of me. Then this summer I tried it again, by the end of summer I had finished Halo 1-3. I'm now a fan. "

Final Fantasy VII. When I was REALLY YOUNG, I thought it was a rip-off of Pokémon. This is before I knew RPGs were a thing
 
Then, for some reason, I decided to rent Final Fantasy VIII and I loved it. I then went back to Final Fantasy VII and enjoyed it.

" Super Mario Sunshine for me, Claude. When I first played I was all like, WTF is this painting and hovering shit?, but after a while it really grew on me and I began to see the games charm. Sunshine's so underrated, I think all Wii owners that have never played it really should... "

Ninja Gaiden 2. I got incredibly frustrated by the difficulty and reached a point where I decided I'd had enough. Came back a couple months later, started to get a better grasp of the combat (by which I mean, read a faq and discovered the on-land charge technique which moves the game from 'nigh impossible' to merely 'hard as hell'), and had a much better time.

" Mass Effect - the original 1.0 PC version crashed and bugged out quite a few times for me, and it got so bad that eventually i was just done with it, also i wasn't digging the game that much in all honesty. Then around November i re-installed it, and not only was there a patch to fix the issues, i also fell in love with the universe itself. "

Diablo.

Twilight Princess. My first playthrough consisted of my yawning 80% of the time while nitpicking at little things that made this the worst Zelda in the series. 
 
Second playthrough..I still think it's the worst Zelda in the series but It's a fantastic action adventure game.

" @Bombs_Away said:

" Halo...Once you land on Halo at the beginning and are running around trying to find the other soldiers that bored the shit out of me. Then this summer I tried it again, by the end of summer I had finished Halo 1-3. I'm now a fan. "

I never saw you as a Halo fan. I learn something new everyday... on the internet. "

Halo CE 
Demons Souls

Borderlands. When I first played it I hated it so damn much. I tried it again, now I love it.

" Mass Effect - the original 1.0 PC version crashed and bugged out quite a few times for me, and it got so bad that eventually i was just done with it, also i wasn't digging the game that much in all honesty. Then around November i re-installed it, and not only was there a patch to fix the issues, i also fell in love with the universe itself. "