Most of my top genres are pretty much out of order and not in high demand right now. I like the Quake 3/Unreal Tournament style shooters, though by this point in time such games simply cannot be found. I really like turn-based strategies with the absolute cliche favorite in Heroes 3, I also like the Action Adventure genre that is still pretty much alive and well these days. I also like the cover-based third person shooter, Gears of War style. To add to the list, I especially enjoy an RPG with a long and good story, not a grind-fest however. And last but not least, fighting games, primarily arcade style, though I pretty much like all of them with very few exceptions.
The ones I dislike playing would be just about all non-fighting sports games, grind-fest MMO games (excluding the ones that actually have a story behind them), everything Guitar Hero related, probably just about any motion control game on the market. There are probably some more to add here but I can't think of any right now.
What I would go on to design and program however is a totally different story. From the game design perspective, I take it as a personal challenge to make the game into something good and interesting, regardless if I find the topic good. If the play testers like it, then I'm happy. A project I had a while ago involved designing an achievement and perk system and a flexible and configurable rule set system in a football quiz. Both football and quiz are not in my top favorites, to say the least, however after we were done with the game and released it on Android and iOS, I was happy to note that it circulated for quite some time in the App Store's top 10 free sports apps.
In terms of programming it's really much much easier, as I tend to see the thing as a system that needs to be built, regardless of genre.