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.
I think I've been at the last level of Gunstar Super Heroes for a few years now. I've also been at the last level of Metal Slug Advance for even longer (since high school at least). I haven't beaten either because the last levels were just too hard, so I shelved them. I plan to beat them someday, but I don't know when that will be.
I stopped playing Phoenix Wright Ace Attorney: Justice For All near the beginning of the last case, because I just lost interest in the game, and the overall series. Part of it had to do with my getting extremely tired of the heavy-handed Ace Attorney storywriting formula, and another part of is was my absolutely hating that stupid fucking Franziska von Karma. Holy shit do I fucking hate her. Well, not really, but when I'm seeing her do shit it just pisses me off, so I stopped playing. Even without her though, the formula has just really tired me out.
I've played Rockman & Forte (Mega Man & Bass) up to the first fortress stage several times, but have never beaten any of the fortress stages because they're hard. Or at least I thought they were hard as a kid; I haven't tried them since elementary school Maybe I'd do better in them today.
I'm in World 6 (I think) of New Super Mario Bros. Wii at the moment. I haven't played it recently because I got back into X-COM: UFO Defense (which would have made it into this post if it weren't for my finally beating it a couple weeks ago). After beating that I wanted more X-COM, so I've been playing Terror From The Deep. Whenever I have free time to play any game (for the moment), I go straight to X-COM instead of any other type of game. Maybe at some point I'll start to get worn out on those games, and will want to play something else again, but that hasn't happened as of yet.
I remember liking the beginning to Wild Arms, but never getting anywhere in it. I can't remember why. So long ago.
I also didn't get through Rune Factory: Frontier. It's the only Rune Factory game released in the US that I haven't beaten. I got to the fire dungeon, and the difficulty ramped up so hard, I got very frustrated and meekly walked away. I went back later and beat that place, but it was years later, and I put it aside again to play things that hadn't (yet) broken my will.
I can't remember if I ever finished the final battle in Skies of Arcadia, which generally isn't a good sign. I remember it being a bit hard, and I also remember that I was playing it years after release, and there was just so much else to play.
Also never beat Muramasa: The Demon Blade, despite adoring that game. I think it's because I saw my husband beat it first. That happened constantly as a child as well. Being the youngest of four, I generally saw a sibling beat a game while I was near the end of it myself. I just got used to almost finishing a game, seeing the ending anyway, and being cool with that.