Rhythm Games: DDR is what I've played the most of, but I also have my fun with Pump It Up, Beatmania (5/7K) and SMX.
More experimental/one-shot titles like Gitaroo Man, Parappa and PacaPacaPassion are cool too. Proud Pop'n Ghetto owner.
SHMUPs: Radiant Silvergun is the videogem ever, the Ray'z series has a wonderful soundtrack, CAVE titles are classics, Darius/Metal Black/Border Down are too hard.
Honorable mention to the wonderful Einhänder. Never 1cc'd a shmup award.
J-RPGs: Xenogears, FF7, SMT3, .hack IMOQ, Shenmue, Drakenier, about time I finished more of those...
VNs: SciAdv, Zero Escape, Higurashi, Fate, Tsukihime, 428, The Silver Case... It's rare for me to not like a VN I finished.
I started many other games, and fancy them without reaching the end: Resident Evil, Drakengard 2, Ragnarök, Mario Sunshine, the list goes on...