I usually don't like putting down games. When I buy a game I try my hardest to finish it. There are still a few games that I just dropped for one reason or another though.
Lets see...
Far Cry 4: I loved the gameplay to death and I liked the story well enough. Unfortunately I got the endings spoiled for me and realized that both of your main quest givers were total fucking insane assholes that make the country shittier in their own ways. I was maybe 50% to 75% done with the main story and I had done almost all of the hunting and other little quests, so I put the game down because it had nothing fun left to offer me. I'd pick the game up again and shell out money for a "join Pagan Min and shoot some guns" DLC in a heartbeat though. I definitely liked him a lot more than that backwards dude and psycho chick that give you quests.
Destiny: I got it for free when I bought my ps4, but didn't actually start to play it until the first piece of story DLC was out. I forget the name but it had to deal with Crota (Krota?) or something. I played with a few buddies and had some fun, mostly because we ripped on the game and I was usually drunk or tipsy when I played. We all got evry annoyed at the lack of variety in the... They weren't flashpoints, I forget what they were called but in them you ran through a gauntlet of enemies and then fought a big boss at the end. Anyway, there were few of those but precious little else to do in the game, especially if you wanted to grind gear. One time we fought the Archon Priest (or something) 4, maybe 5 times in a fucking row. Me and my buddies eventually hit the point where EXP doesn't give you levels anymore, but we could never find any fucking gear to give us more "light levels" or whatever. We played for one more month after that and only one of us got the gear needed to level up, so we just quit playing. I went back to playing Halo and Borderlands and had much more fun than I ever did with Destiny.
Dragon Age Inquisition: I bought this game day one of release. And. I. Hated. It. I put it down before I even got to Skyhold, I think. I found it boring, the combat was not to my liking, and I was just not invested in the story or characters at all. I tried to play it again earlier this year and I actually made great progress. I wasn't exactly having fun but I wasn't hating the game either, it was a good time sink, which I needed at the time. So I grinded, did secondary quests, main quests here and there, and did lots of dragon hunting. The dragon battles, at least early on, were the best part of the game, buuut they got pretty boring too after like the fifth or sixth dragon battle. I got more into the characters, like Josephine, Solas (especially Solas), and Cullen. I didn't really get into the other characters though. Iron Bull was okay, pretty fun, but my PC already filled his role and did it better. Cassandra was an important part of my team, but I found her character to be kind of abrasive and needlessly antagonistic. Varric was just not as fun as he was in 2. I hated Sera (might not be her name, she was the lesbian elf rogue with the annoying voice and immature outlook on literally everything). I never used Cole, I didn't dislike him but I wasn't a fan of him either.
I did everything I could up until the Winter Palace mission or whatever, including the Grey Warden story line, and then I just got way too bored. The main story was not gripping me, I didn't care about most of the characters, and the gameplay was just meh. Put it down for probably the last time at that point. I don't think I'll be picking it up again.
I think that might be it. I usually force myself to play through games I find boring or kinda bad just to make it worth the money I spent, but the games above just had one too many flaws for me to force myself to play to completion.