I will let you define "love" however you want, but I'm not talking about the typical backlog most of us have. I'm talking about games that really stood out for you in some way, and you might even call one of your favorite games, but you still didn't finish for one reason or another.
I'll also let you define how much time has to pass to say it is "stopped", but personally I'm not going to include something like Pushmo which I feel like I'm still actively into, in some form. I'm thinking more of games I haven't played in months / years.
Here we go...
Mike Tyson's Punch-Out!! - I think the main reason is that it is a game where you can't really do much else if you are stuck other than keep playing the guy you are stuck on over and over and over. I think I got up to Mr. Sandman and never finished. It doesn't help that it knocks you back a few guys when you lose enough times.
Castlevania III: Dracula's Curse - It's hard as balls. Also you have to go through the entire stage you are working on every time you run out of lives, ug.
Ghosts 'N Goblins - Also hard as balls.
Zelda II: The Adventure of Link - Again, hard, but more than that... confusing and way too much dying and having to navigate from the beginning all the way back to the dungeon you were working on.
Super Turrican - I guess just the fact that you have to start from the beginning every time you run out of lives. I don't have much patience for this nowadays.
Final Fantasy: Crystal Chronicles - My cousins and I got very close to the end, but we ran up against a boss that was both long and nearly impossible. Each attempt took like a half hour, so we just kind of gave up after 5 or 6 attempts and never went back.
The Legend of Zelda: Four Swords Adventures - In this case I think it was just the fact that me and my cousins who got pretty far into it stopped hanging out together as much. Haven't really had a group of people to make any more progress in it. Would love to someday, but I kind of don't see that happening.
Monster Hunter Tri - I really like this game, and I'm not really sure why I stopped? I guess it had to do with getting a decent amount into the single player and then shifting over to playing primarily online. But at a certain point I just couldn't keep up with everyone I was playing with online and didn't want to be the guy making everyone else do lower level quests. And I kind of want to go back to single player, but I just never did. This was probably mostly due to the string of awesome games that released soon after. Maybe I'll go back someday.
Kirby's Epic Yarn - Started playing with my girlfriend, and I think she never really got into it. So... put it on the side, on occasion played it with my nieces and nephews, but for the most part haven't really touched it since. Something about this game feels like it needs to be played co-op to get the full enjoyment, but I don't really have anyone to play it with.
Punch-Out!! - Same idea as original Punch-Out!! Basically I got to the "rematch" Aran Ryan and never got any further. But it was also timing... I don't think he was super tough, but other games came around and I never quite went back. Still, love this game and hope to finish it someday.
BIT.TRIP BEAT - Never quite could finish the 3rd stage. Got very, very close to the end at times, but never pulled it off.
Demon's Souls - Awesome game, but I just don't really like how brutal it is. It's not even necessarily that hard, just very unforgiving when you die. Way too many super long, drawn out stretches just to die and have to do it all over again. Possibly with half the health.
When I was younger, my dad and I went to the flea market to buy some N64 games. On that day, I picked up 3 games: StarFox 64, Pokémon Stadium and Bomberman 64.
My father had tested all three and nothing seemed wrong, so we I went home and, after dinner, began to try the games out. Pokémon and Starfox were fine, but Bomberman had a little problem. The whole game was in Japanese. I don't know if N64s made in Brazil could play Japanese cartridges, but that was what have happened.
I was like "Oh, big deal" and began a new file. It was an awesome game and I played through most of it, until I got stuck in the level that was a big island on top of all the sky islands of the world. Didn't know about the internet back then and signs and characters didn't help either.
After giving up the adventure mode, I left the game aside and would only use it for multiplayer when friends would come over. Unfortunately, my friends would almost always bring Super Smash Bros, so Bomberman was pretty much left to dust.
Now that I talk about it, I should get to that again, someday.
Skyrim - The game is freaking long when you try to do every sidequest you come across... And I just recently started back at school and have had very little free time, so it's on the back burner until Christmas break or something.
Okami - Well, to be fair, I didn't quite love this game. But I did really like it in the beginning. For the first third of the game, I was really intrigued with it, and despite thinking Issun is worse than any Zelda companion ever, I still enjoyed it. But then, after finally defeating the ultimate evil that was threatening all of these people that I had grown familiar with and fond of, I learned that there was another ultimate evil threatening another land populated by another group of people and I "fell out of love" with the game pretty fast. And then I was faced with the same situation yet another! It just felt like the game was too long... Like it was artificially padding itself, and this artificial padding worked to the detriment of everything I'd done before it. So that made me just not want to keep with it, especially for fear that the game might do it again to me (though I expect that was the last time).
Bowser's Inside Story - I don't know what happened with this one. Maybe it was another repetition thing. Using giant Bowser and the DS gameplay gimmicks are really fun the first few times, but it kind of wears on you. I want to go back to this one, but I've just never gotten around to it.
@Zero - No shame in using a guide to get you through Adventure of Link if you absolutely have to. It still takes plenty of skill to take out all of the enemies and bosses even if you have "someone else" doing the dungeon and overworld bits for you.
And as for Four Swords Adventures, I had more fun with that game playing it single player than multi-, so I definitely wouldn't say you have to find someone to play the game with you. Just switch to single player mode.
The only game that I loved but never finished was Battletoads on the NES. It has so much originality for a beat 'em up, but it's also close to impossible to complete.
EDIT: Actually, I also thought of Zelda II. I can't believe I forgot about that one. I also loved that game as a kid, but it's the only Zelda game that I couldn't finish due to the high difficulty towards the end of the game.
Hmm, and now I'm recalling Darkwing Duck on the NES. Rented it, got all the way to the ending, was confused about what to do, turned it off, and in those days... when you turned it off, you pretty much had to play through the whole game again.
OH... Super Ghouls 'N Ghosts for sure. Got to the end... THE SECOND TIME, but couldn't figure out how to beat the mini-boss leading up to the true end boss using the stupid bracelet which only shoots like 3 (in-game) feet in front of you. Gave up, never felt like going through the whole game again just to get stuck again. I have heard there is a cheat to warp to the end though...
Fire Emblem my memory card fucking sucks and crapped out 3 chapters before the end. Demon's Souls I was halfway through the game my PS3 fucking sucks and crapped out yellow light of death. Skyrim I wasn't playing to beat the mainstory but I'd go to it between games to do side quests. I was in it for the long haul. Red Dead Redemption I stopped playing because I was really excited to play Demon's Souls and Skyrim(see above).
Eternal Darkness somehow my file was deleted. I looked up a strategy guide and I was about an hour or 2 before the end.
Many others life
EDIT: It also doesn't help that I like to take my time with many games to take it all in or interact with everything. I'm not one to quickly rush through levels.
Metroid Prime 3: I got to the part where you have to recover all of the artifacts. The clues were so vague, and there was so much backtracking involved, it turned me off completely to finishing what was a pretty good game. Oh well.
It's weird, I actually like those bits of the Prime series. They're kind of like deciphering the cryptic clues from the original LoZ.
That being said making them mandatory and placing them right near the end of the game ruins the pacing somewhat. Had they been optional and resulted in some sort of uber beam or something, I think the idea would have been received
@Zero I agree with V_s here. I just played Four Swords Adventures from start to finish in single player for Backlaugust. You can totally go and get it done in single player.
For me, I'll probably list Final Fantasy VII and Baiten Kaitos. In both games I got all the way to the final boss but got curbstomped. In the case of FFVII my save then corrupted so I haven't gone back, in the case of Baten Kaitos....well I just gave up & got distracted by RE4 instead.
Metroid Prime 2: Echoes - Twice now I have gotten to the very end of the game, but I never even tried the final boss battle. The first time, another game ended up coming along and distracting me (Minish Cap, I think it was?) and the second time I ended up letting somebody borrow my GameCube. Bad planning on my part.
Crackdown - I got addicted to this game a couple of years ago, and I played the hell out of it but never finished it. Looking back, I honestly have no idea why.
Eternal Darkness: Sanity's Requiem - I really enjoyed the beginning, but early on my memory card got corrupted and I couldn't save.
StarTropics - I think I got stuck somewhere and then never came back to it. I'd love to go back, but I'd have to start it all over again and I'm way too lazy for that. I'll probably buy it if and when it comes to the eShop.
Bit.Trip Fate is one for me. When I think of my backlog, this often goes forgotten. I just didn't have nearly as much fun as I thought I would after Bit.Trip Runner. And I have no desire really to complete it.
I'm good about finishing games I love (and not bothering with games I hate). The following are games I really enjoyed for a while but abandoned for whatever reason.
Star Wars: X-Wing - Great game but it was too hard for my 8 year old mind.
Star Wars: TIE Fighter - See above.
Burnout 3: Takedown - The rubberband AI just got ridiculous.
Frequency - Disc read errors.
Final Fantasy III - Game save battery died while I was recollecting characters after the midpoint. Then I bought it again on GBA and just kinda grew bored with it around the midpoint. Maybe someday I'll get it on the VC and try again.
Elebits - The mid-game slowdown was just ridiculous and it seemed like it was started to pad itself out.
That reminds me, I stopped playing Final Fantasy II aka IV because I got stuck at this queen that seemed impossible. And then years later my brother informed me that she was an optional side quest boss. And then I went back to play it again but the battery had deleted my save.
I'm not sure if I would say that I loved the game though. It was good, but not one of my favorites.
To be honest, one of the big reasons I don't complete games is because I get sick of playing them by myself. If Steph doesn't want to come along for the ride, I usually just skip it and do something else. That's why the Tingle Tuner has to make a comeback one of these days. I can guarantee you I'd be through Skyward Sword right now if they'd included it.
The only game I can think of where I was really enjoying it, but stopped and came back to it later, was Bioshock. I kept putting off buying it because Metroid Prime 3 came out around the same time, and the next time I wasn't really busy, Galaxy came out. I played a little bit of Bioshock once I finally got it, but quickly got busy again and the next time I had a window of opportunity -- you guessed it, Brawl came out. And then GTA IV. And then something else. I never actually got around to finishing it until last year. Which is too bad, because I really liked it. I just never found the time for it.
Other than that, I finish everything I start unless it's boring me. I'm slogging through Assassin's Creed right now, after losing interest about a year ago now. I still don't really like it a whole lot, but I'm hellbent on finishing it before playing the second one.
My gaming resume is riddled with unfinished JRPGs. FFVII, Skies of Arcadia, Tales of Symphonia, FF Tactics (yes I know it's different but I'm including it anyway), Golden Sun... I enjoy them for a while but either I lose interest or life prevents me from gaming for a while. When I try to pick them up again I'm so unskilled in that particular game's mechanics that I get destroyed in the first random battle, and I don't have the patience to repeat the grind of getting back to where I was in a new game.
I finally cracked open Xenoblade, though. Hopefully I'll be able to complete my first JRPG since Chrono Trigger.