My top five, no particular order:
First-person shooters
I think I fully fell in love with FPSs with Dark Forces. It felt like such a fleshed-out and immersive way of playing a game. It's been one of my favourite genres ever since, in part because the genre is typically on the cutting edge of new technology. Highlights include - Halo: CE, Halo Reach, Crysis, Black, Half Life series, Call of Juarez Gunslinger
Third-person action-adventures
I'm being quite broad with this as I'm pretty much including any third-person stealth or action game. I like the 'wide linear' style of design, so recent high points are the last few games from Naughty Dog. Other highlights include - Metal Gear Solid 3, Tomb Raider Anniversary, Devil May Cry 3, God of War, Hellblade
Walking sims
I'm serious. I think games can be a great vehicle for delivering an interesting or impactful story, and walking sims often get me really immersed in their setting and premise. Highlights include - Journey, Everybody's Gone to the Rapture, The Vanishing of Ethan Carter, Tacoma
Horror games
One of my favourite genres in general, but games in particular have the capability of being incredibly involving because of the medium. They have a way of worming their way inside you head like few other genres. Highlights include - Silent Hill 2, Resident Evil 1 & 2 remakes, Dead Space, Lone Survivor, Soma
Action RPGs
Again, I'm being kinda broad with this definition but I love the idea of having a huge world to explore, enemies to fight and dungeon areas to explore. Highlights include - Zelda: BotW, Horizon Zero Dawn, Dragon's Dogma
Honourable mention: Karting games. I just wish as a genre if had more representation.
Least favourites, no particular order:
Card games
MMOs
Simulation games
Super-grindy gatcha shit. Doesn't matter the genre
Sports games. With the exception of tennis and billiards I basically dislike all of them (but then I don't like sports in real life either)