I play lots of games. I try to be open to lots of different genres and types of games, as long as they seem smart and good (for lack of a better word). There are certain types of games that don't appeal to me though, like stuff based on pointing and clicking and hitscan (90% of moba's, mmo's like warcraft, etc.), RTS are fine though in that regard.
I also love 2d games. I feel that 2d games have an emphasis on precision and movement based play that give incredible depth to the simplest game systems.
I prefer combat to be based on a combination of reflexes and strategy, and I like games that emphasize improvisation over planning and static memorization. I think excitement and hype are the most important things in gameplay for me, with excitement being best brought about through challenging gameplay and penalty for failure, and hype by general resonance with the game mechanics.
Genres of choice I guess would be:
Fighting games (generally prefer air dash fighters over street fighter/kof style stuff, but I like those too)
Shmups (Used to prefer traditional style over bullet hell, but now I'm leaning towards the other way around. I still love Gradius and Rayforce though)
RTS (Only played Starcraft though unfortunately lol)
Oldschool Fps (FPS of the Doom/Quake school of design)
3d Action games (heavily depends on the type of fighting system though)
Adventure/Action Rpg (see above, also the exploration and story should also be good)
Turn based rpg/Dungeon Crawl (Assuming it's actually well designed and not just a grinder. Shin Megami Tensei and Etrian Odyssey come to mind)
Notable Games/Series:
Odin Sphere (Brilliant Concept, lacking execution, story and atmosphere make up for it though)
Gradius (I don't think there's a more perfect blend of reflexes, strategy, and variety in any single player game)
Contra (Don't think I've ever played a more driving and intense side scroller)
Touhou (I play lots of bullet hell shooters, but I particularly enjoy Touhou due to the excellent use of rng in patterns, and the creativity of patterns and level design that the series has maintained over 14 freaking games)
Shin Megami Tensei (Beautiful atmosphere, dark story with an undercurrent of hope, great game design, and a unique approach to ethics and morality in video game storylines. It's a really fucking good series)
Doom (A 3d shmup that brings together reflex based combat, strategy, exploration, secrets, and resource management together into one of the most fun games ever made)
Phantasy Star (both the rpg's and the action mmo. Great world, great gameplay.)
Kingdom Hearts (Story was good only for the first game IMO, but the gameplay and boss fights are always fantastic)
Anything by Platinum Games (best hack and slash, best shooters, best party games, pro games for pro gamers)