I like this topic, although I feel like genre alone doesn't speak adequately to the different fan bases. You could group Breath of the Wild, Sea of Thieves, and Uncharted 4 under action-adventure, but all three play very differently due to the mechanics and designs underpinning them.
Back on-topic...my favorite genre is action, with a special focus on action-adventure. Basically anything where there is a balanced mixture of real-time action, puzzle-solving, and exploration. A few games that typically fall under "shooter" could in theory be labeled action-adventure, like Half-Life 2 and BioShock. Some of my favorite series under this banner include The Legend of Zelda, Metroid, and Resident Evil.
Another subset of action I love is platformer, which at times overlaps with action-adventure. Series like Metroid, Castlevania, Ori, and Guacamelee arguably belong under action-adventure, but they certainly focus on platforming to some degree. Even 3D platforming games like Banjo-Kazooie, Psychonauts, and Super Mario Odyssey -- all favorites of mine -- share something in common with action-adventure. My favorite platformer franchises include Super Mario, Donkey Kong, and Rayman.
A third favorite: role-playing game. This includes "classic" turn-based affairs based on the pen-and-paper variety and their cousins in the action-RPG camp, which also have a lot in common with action-adventure. I enjoy assembling a party, managing classes, upgrading characters, going on quests, exploration, etc. While I certainly gravitate toward the instant gratification of real-time action (see above) I also enjoy the tactical, methodical process of planning and executing a winning strategy in a turn-based environment. Among my favorite RPG brands: Final Fantasy, Xenoblade, The Elder Scrolls, and Souls.
I took a look at my top 20 games from mZuzek's Annual Greatest Games thread and found that 16/20 games are either action-adventure, platformer, or RPG, or some combination of the three.
My favorite game-maker is Nintendo.