I'm into RPGs, especially JRPGs. Stuff like the Mother/EarthBound series, Persona, Pokémon, and Shin Megami Tensei, are some personal favorites. I finally got into Dragon Quest with 11 and want to get into some of the older games. I've been watching someone play Like A Dragon: Infinite Wealth recently and it has gotten me wanting to get into the Yakuza/Like A Dragon series from the start because I like what I see.
I have a particular fondness of turn-based tactical RPGs like the Fire Emblem series and the first couple Shining Force games. Triangle Strategy, Final Fantasy Tactics, etc., give them to me.
Fighting games and side-scrolling beat-'em-ups were two of my introductions into the world of video games, so I have a fondness for them. I'll play most fighting games, stuff like King of Fighters, Mortal Kombat, Soul Calibur, Street Fighter, Tekken, etc. Super Smash Bros. games aren't traditional fighters, but I'll mention them here too as they're pretty enjoyable. As for beat-'em-ups, Streets of Rage, Streets of Rage 2 and Golden Axe were my introduction, I played Scott Pilgrim vs. The World: The Game back when it first came out, and I've also played stuff like Streets of Rage 4 and River City Girls in more recent years.
Another early introduction to video games for me were puzzle games thanks to the video game Columns. I enjoyed the Animal Crossing Puzzle League minigame in Animal Crossing New Leaf and it opened my eyes to the Panel de Pon style. Tetris 99 being (partially) free on the Switch got me into Tetris and I find it to be a nice, quick time-killer. I've also played Dr. Robotnik's Mean Bean Machine a few times via Sega Genesis Classics and that's fun too.
I've also discovered a fondness in recent years for pinball video games, though I haven't really dived too terribly deep into those yet. My older sibling had a cool game called Dragon's Fury for our Sega Genesis and I always thought it looked cool, getting into it myself years later. I found out that it was actually a port of a game called Devil's Crush and that the people who made that also made a few other neat pinball games called Alien Crush and Jaki Crush. A few years ago I learned of a game in the same vein called Demon's Tilt, though I only just recently got it on sale since the normal asking price was a bit more than I wanted to spend on this sort of game. I might have to look around for more neat pinball games.
I'm not too into simulation games, but I'm quite fond of Animal Crossing and I like Stardew Valley.
Also, shoutout to visual novels since I've seen them mentioned here. I've only played a few, but they're fun.