Apart from the notable "generic" genres (basically, Sports and Realistic FPS - though I do like MMOs), I have a particular distaste for RPGs. Specifically JRPGs - the combination of long-winded stories with tedious battle systems just sucks any interest I have in the game away. It's hard to pay attention to a story when it's getting interrupted every 15 seconds just so the game can say "AND THEN THEY FOUGHT A THING" and you spend at least a minute going through the fight. Though pretty much ALL games with long-winded stories which feel very seperate from the gameplay apply here - it doesn't matter if it's Persona 4 Golden, Paper Mario, Final Fantasy, Fire Emblem Awakening or Pok?mon Alpha Sapphire... each I've tried, and each I've ended up just taking an extended break somewhat early in, coming back and having no idea what the hey was even going on with the story. (Just to prove how much this bores me: Literally the only Final Fantasy titles which kept my interest were the Crystal Chronicles games)
Very rare do I care about a game with heavy emphasis on story, but it helps when the story is seamlessly integrated into the gameplay. Bastion had a fantastic way of going about storytelling with a narrator who talks over your gameplay, reacting to the things you do and telling you about the areas you're exploring and your goals. Undertale also had an interesting battle system which also worked the story elements into it, often having story take place during battles without interrupting it (so it never felt like the battles were interrupting the story or vice-versa)
Another genre I don't care much for is RTS and Strategy games. I don't know what it is, managing a bunch of units should interest me, but I've never really cared to get into any RTS or Strategy game with the sole exception of Age of Empires 2. (And even then, I can barely beat Easy CPUs.) I... honestly couldn't tell you why these games don't interest me. But I've tried to get into them... and they just didn't gel at all. It's weird - the idea of commanding a whole army to do your bidding sounds very fun to me, but the execution just never interests me at all.