The sealed blob monster in Skyward Sword. It was first because the motion controls were screwing up, with me. But I just got so fed up. I was like "Why the fuck is this mini boss in the game 3 times?" I was getting bored of the story during the middle. This monster triggered me to quit on the game. I still haven't beaten it. Going back and forth. The sky area was pointless. A lot of the characters were boring/annoying. I just had enough. I even remember thinking: "I'd rather be Zelda right now. She's going threw dimensions. While Link is dealing with this black monster. And Groose is wasting my time."

I was a diehard fan of final fantasy, played every previous game multiple times until final fantasy 12 -- I tried so hard to like it and be interested in the story, but ended up quitting about 30 hours in because I found the story too unbelievably boring.

Once I started playing as Raiden I dropped MGS2.

Yes, my most recent game is Bravely Default with the awful story, making you do the same things again D:

Yes, for story/gameplay FF XIII.
Couldn't bring myself to continue passed a certain point and sold the game.

Saya no Uta. For some reason I tought there was no sexual content, especially that early in the game. My gf was by my side when an hentai CG popped up which was embarassing enough for me to quit playing and I never played again.

This is more often than not the main reason I stop playing certain games.

MGS4
MGS5
GTA4
LA Noise
Watch Dogs
Bayonetta, Amazing gameplay here but abysmal story and dialogue .

Fair enough, but it isn't like most of the other hack and slash genre fairs any better as far as storytelling. Even the series that stated it all (Devil May Cry) has abysmal storytelling and dialogue. 

https://www.youtube.com/watch?v=H8qG4AlK1qk

Also, I'll admit that when the story in LA Noire required me to examine closeup the naked body of a brutally murdered woman, I called it quits. Just not comfortable doing that.