As a huge Halo fan, my vote is for Martin O'Donnel. He has consistently produced amazing music for the series, from moody ambient cues to epic pieces and even jazzy film noir music in ODST.
I also really liked what Petri Alanko wrote for Alan Wake. The score for the first Fable is another peronal favourite (music by Russel Shaw and theme by Danny Elfman). Although I don't enjoy the sequels on quite the same level (the same goes for the games themselves).
I have to split my vote between the western composers people are more familiar with and the eastern (Japanese) composers who have been at it for decades.
The West: Jeremy Soule - No one makes samples sound more like a real orchestra. James Hannigan - His "Harry Potter" video game scores are better than the actual film scores. Jason Graves - Very versatile, and not afraid to experiment (a la "Dead Space"). Honorable Mentions - Jamie Christopherson, Mark Griskey, Richard Jacques.
The East: Hitoshi Sakimoto - His solo scores are increasingly rare, but they're always fantastic and propulsive. Yoko Shimomura - No one can handle light and dark in the same score as well. Nobuo Uematsu - His recent scores aren't as consistently great as his old ones but show a real maturation of technique. Hiroki Kikuta - An absolutely unique and infectious musical personality.
While Toshiyuki Watanabe is great, he didn't really have anything to do with the track from Shenmue posted above. That piece was composed by Takenobu Mistuyoshi, and arranged for orchestra by Hayato Matsuo. Watanabe only contributed a single track to the Shenmue Orchestra album, though he often seems to get credited as the sole composer.
Nobuo Uematsu - His recent scores aren't as consistently great as his old ones but show a real maturation of technique.
It is quite a shame that he went downhill so far since Blue Dragon and Lost Odyssey. I was expecting The Last Story and Final Fantasy XIV to be similar but they fell flat. I hope he can pull out something amazing for his next score.
I'd say my favorite that provides the most quality scores is Hitoshi Sakimoto. There are just so many good scores he wrote. Other composers like Yasunori Mitsuda have a few good scores (Chrono) and then dropped off in quality for me.
I think Masashi Hamauzu is a very talented composer but only when aided properly by some great arrangers and orhcestrators. His work in Unlimited Saga and FFXIII really stands out as high quality. Naoshi Mizuta has shown on Final Fantasy XIII-2 some great composing chops although I suspect that similarly all the good orchestral stuff is arranged by Yoshihisa Hirano.
Other composers like Yasunori Mitsuda have a few good scores (Chrono) and then dropped off in quality for me.
He barely writes anymore, too. Aside from tiny contributions of one or two songs, he hasn't written a full score since 2008.
I think Masashi Hamauzu is a very talented composer but only when aided properly by some great arrangers and orhcestrators.
A lot of film score fans seem to like that guy, but I generally can't stand him. All the ingredients that make a lot of Japanese video game music great are there, but they're mixed together all wrong, to say nothing of his allergy to hummable themes.