Fairfox: teh main character = biggest douchebag in teh world (srsly, die).
This kind of thing, where I can't relate to the main character, also tends to turn me off to the game to some degree. If the main character isn't someone I would be comfortable having as a friend in real life, then that does hurt the game for me. I've heard, for example, that in at least one of the modern Persona games (I consider Persona 3 to be the first modern Persona game), that the main character is transphobic at at least one point.
A few other things:
* Straight romances are something I can't relate to. If the game (or movie) makes such a thing a big part of the plot, then it becomes significantly less interesting to me. (Same-sex romances, especially lesbian romances, are good, however, but they're few and far between.)
* Negative portrayals of LGBT characters (like making them villains, particularly stereotypical ones) is also a big negative, unless they're balanced out by positive ones. (I actually ended up de-whitlisting A Hat in Time after hearing about something like this happening.) This could reasonably be extended to other minorities (like having characters with mental illness), but it doesn't matter as much for me (though it might for some other gamers).
* If the game, for plot reasons, takes away a mechanically interesting character, that is, again, a big negative. (This happens in Final Fantasy 7, for example.) Exception, of course, if the game immediately gives you a replacement character with similar gameplay characteristics.
* If the game has me create a character, but requires that the character be male, that is another significant turn-off for me. Even worse is if the game is like Eschalon Book 1, where there's a gender option in character creation, but if you try to change it, the game gives you a rather flimsy excuse and doesn't let you change it.
Leroux: That being said, I think all games get repetitive after a while, even without a story.
Sometimes, repetitive gameplay is what I need, so having a game be repetitive isn't always a bad game. It's especially nice when, by repetition, I can keep increasing some numbers, particularly if the math behind those numbers is complex enough to be interesting (hence why I enjoyed Cookie Clicker).