Metal Gear Solid.
I think I would go along with it and be cheeky, but I just cant get over the fact that the game somehow wants you to take it seriously? or at least the game does.
and then you try to figure out the point of it all... and just realize that "hey, Kojima, I think you have enough money to hire a good editor" because you might have a good story to tell... but its lost in a giant flood of verbal diarrhea.... that I stopped caring.
I also skipped the cutscenes in MGS4, and still liked the game. I didnt know what was going on entirely, but I was much more entertained.
Final Fantasy and Indigo Prophecy are also notorious for having plots that make me think.
"hmm, yes, ok Im following you"
then at some point it turns to...
"well thanks, I was almost enjoying the story, now its just preposterous"