I love video games so I'm willing to give most things a chance. In general, my least preferred genres would be:
First Person Shooters - I like the concept, and I even own a few (BioShock trilogy, Call of Juarez: Gunslinger, Resident Evil 7 of course), but something about the "floating arms" perspective throws me off. I like to see the avatar of my character on my screen, and have a much wider Field of View for combat. (so maybe it's less about the "floating arms" and more about what I feel is a very narrow FOV for some of the FPS games I've seen). So, funny that I don't really prefer or even like First Person Shooters, since I love Third Person Shooters.
Turn-based Japanese Role-Playing Games - I generally like my games to have some sort of "immediate" action that I can go to at my pace, usually something tightly timed and reaction based -- platformers, fighting games, shmups, shooters, etc. Turn based JRPGs seem to me like a bunch of never-ending menus, and the flow is dictated by the game's pace, not by me. I am willing to give this genre a chance though, and I own 3 of the key Super Nintendo JRPG carts (Final Fantasy VI, Super Mario RPG, and Chrono Trigger... god, I hope I like them, if I don't I'm gonna have to sell them off, LOL).
For me it's easiest to play a genre I don't like if a game in a series I love somehow switches over to that style. Resident Evil and Yakuza are my two favorite game series, and they've switched from genres I love (TPS and beat em up respectively) to genres I generally don't like (FPS and JRPG respectively). But my love for the series trumps my dislike for their new genres, so I still play and enjoy them.