Anime, Action & Adventure, Card & Board, Casual, Free to Play, Multiplayer, Puzzle, RPG, Strategy, as well as those with both Steam achievements & trading cards plus some Visual Novel types, to a lesser degree, are my main gaming categories. I also like playing Shooters and Fighting games, but usually I stick to consoles with those.

I'm not really into Tower Defense or Racing games, though there are some games which might catch my attention once in awhile like "Dungeon Defenders" did. Chaotic race/kart games such as: "Sonic & All-Stars Racing Transformed", "Mario Kart", and "Diddy Kong Racing" on Nintendo consoles were fun, but it's mainly the more realistic race games I shy away from.
Sports games I don't play at all. I never really had an interest in them growing up, much less enjoy watching one being played, even though I like shooting some hoops myself or having been on my middle school's trek and field team when I was younger. I frequently enjoy playing Table Tennis/Ping Pong with family too. Playing a video-game of these just doesn't hold my interest.

MOBA games I may dip my hand in every now and then, but it's generally one I steer away from. This is due to the teamwork element often being a major requirement for victory in most cases, more-so than the FPS multi-player games I'm more willing to play. It can end in a headache or rage-feast for me and makes the experience less enjoyable when matched with certain "toxic" players, while I'm trying to learn the game still. I just can't commit to constantly learning to play and getting better at it with those scenarios in mind, even if I love the art or certain characters. "Smite" is one I piddle with, but I've stuck to Arena on PS4.
I suppose RTS games can be thrown in this category of steering away from as well. The last time I really got into playing one of them was "Starcraft: Broodwar", if that says anything. Playing against the A.I. can only take you so far in fun and going against friends all the time, while avoiding bad players online, can get stale if you know each other's tactics too well. Let us not forget that with RTS games, your ability to micromanage or macromanage can also hinder your experience. I tend to tunnel vision too much.

Platformer types are hit and miss. Playing the Super Mario games when I was a kid was a blast, but nowadays it just doesn't have that same appeal to me as getting into an RPG or action filled games like an online FPS, such as the "Battlefield" games. The "Shantae" series is one that has my eye, and I did somewhat enjoy playing "Spelunker World" with friends on the PS4 for a time though.

Bullet Hell games I just plain suck at and likely don't have the reaction to be nearly good enough to progress and have meaningful fun with them. To add to that, I could put something like "Super Meat Boy" in the same tier for me. While I don't mind platformer games, the more Difficult styled ones, which require repeat deaths to learn, are a nuisance I don't like dealing with. Also, Permanent death games as well as games which feature an always Friendly-Fire on multi-player are a no-thank-you.