Votes counted up to this point. I'm also going to be periodically bumping this thread up so as many people see it as possible before the deadline.

Nobuo Uematsu (10 pts)
Yoko Shimomura (9 pts)
Jeremy Soule (8 pts)
Michiru Yamane (7 pts)
Shoji Meguro (6 pts)
Motoi Sakuraba (5 pts)
Yasunori Mitsuda (4 pts)
Yuzo Koshiro (3 pts)
Hayato Matsuo (2 pts)
Akira Yamaoka (1 pts)

Nobuo Uematsu

https://www.youtube.com/watch?v=iEGRZ8itn7g

edit (fixed)

You'll have to swap a few of those. McCreary, Otani, Gregson-Williams and Zimmer aren't really video game composers, since they work mainly in film and TV with video games being more of a side thing for them. As a general rule they have to have at least 10 video game composing credits to their name to count. The rest are good though.

1. Yasunori Mitsuda (10 pts)
2. Nobuo Uematsu (9 pts)
3. Koji Kondo (8 pts)
4. Hitoshi Sakimoto (7 pts)
5. Hayato Matsuo (6 pts)
6. Keiichi Okabe (5 pts)
7. David Wise (4 pts)
8. Michiru Yamane (3 pts)
9. Christopher Larkin (2 pts)
10. Miki Higashino (1 pts)

I can only think of six at the moment:

1. Kenji Yamamoto

2. Koji Kondo

3. David Wise

4. Yoko Shimomura

5. Grant Kirkhope

6. Alexander Brandon

1. Nobuo Uematsu (10)
2. David Wise (9)
3. Yoko Shimomura (8)
4. Motoi Sakuraba (7)
5. Michiru Yamane (6)
6. Koji Kondo (5)
7. Hiroshi Kawaguchi (4)
8. Jun Senoue (3)
9. Yuzo Koshiro (2)
10. Tim Follin (1) 

Nobuo Uematsu said if there was one piece of music he wanted to be remembered for it was the main theme from Final Fantasy. He refined it from game to game until the version in FFVIII where he considers it to have reached its peak, and I can't disagree.

David Wise, I think he named this track as the one he was most proud of. It was a real challenge to do on the SNES, maybe not his most popular, but very good nonetheless.

Yoko Shimomura, could easily be in second place, she has composed for so many games, Street Fighter, Mario RPGs, Final Fantasy, the list goes on. Oh and Kingdom Hearts.

Motoi Sakuraba, insanely prolific so some of his music ends up sounding very similar, but I can't complain about it if it's so good

Michiru Yamane, I couldn't choose so here is the first area of one of the best games ever.

Koji Kondo, probably the most widely recognised videogame composer (by his music anyway) and for good reason

Hiroshi Kawaguchi, a Sega arcade legend, also part of the S.S.T band at Sega

Jun Senoue, mostly known for Sonic music, which he does very well, but here is Victory Goal and a slower acoustic piece too

Yuzo Koshiro did Revenge of Shinobi, Streets of Rage and even a bit of Castlevania

Tim Follin's unreleased Mega Drive/Genesis soundtrack, like always, he pushes another old console further than most other composers. His work on Plok was a direct inspiration for David Wise to up his game since he couldn't believe what Follin could do with the SNES.

No worries. I'm keeping an eye on people who tag the thread for later so I can remind them at some point if necessary. 

On a side note, there are already well over 50 different composers who've gotten votes from people, which is really cool to see. We might get to a point where I'll change this to a top 50 list.

Here's my top ten composers. Nobody comes close to Uematsu in my mind when talking about great video game composers, but there are so many amazing composers to choose from that picking just ten is really difficult for me. Had to leave out a lot of composers whose work I love.

1. Nobuo Uematsu
2. Jeremy Soule
3. Yoko Shimomura
4. Yasunori Mitsuda
5. Motoi Sakuraba
6. Hitoshi Sakimoto
7. David Wise
8. Michiru Yamane
9. Frank Klepacki
10. Masayoshi Soken

Koji Kondo
David Wise
Grant Kirkhope
Nathan McCree
Satoshi Okubo
Yoko Shimomura
Taro Bando
Michiru Yamane
Nobuo Uematsu

Hopefully these all meet the criteria. I wanted to put someone who worked on the original Resident Evil, but there's a few names and I'm not sure who composed what.
I'd like to put someone.

1. Yoko Shimomura (10 pts)
2. Nobuo Uematsu (9 pts)
3. Keiichi Okabe (8 pts)
4. Masakuzu Sugimori (7 pts)
5. Takeshi Tateishi (6 pts)
6. Jesper Kyd (5 pts)
7. Shoji Meguro (4 pts)
8. Koji Kondo (3 pts)
9. Martin o'Donnell (2 pts)
10. Michiru Yamane (1 pt)