SacremPyrobolum said:
Shiro Sagisu is the guy behind the OST of animes like Neon Genesis Evangelion, Bleach and some others. He works mostly with Orchestrated music, at least from the animes I know, but there is a lot of variety of themes in his music.
Here are some examples from NGE, with very different themes:
"The Beast"
http://www.youtube.com/watch?v=nt4ldDExzhU
"Crime of Innocence"
http://www.youtube.com/watch?v=5vAj9kDoeac
"Do you love me?"
http://www.youtube.com/watch?v=yMPRMKUQLM0
And here some from Bleach:
"On the Precipice of Defeat"
http://www.youtube.com/watch?v=PLyi5xHtkb0
"Whisper of Apocalypse"
http://www.youtube.com/watch?v=REHHlBbf6nM
"Clavar la espada"(This last one is my favorite. Is flamenco inspired, with a nice acoustic guitar.)
http://www.youtube.com/watch?v=suwfJMiXauU
Yuki Kajiura on the other hand I know from the "Noir" anime , but she's also the one behind the Hack anime and the entire OST of Xenosaga III.
Here's my favorites of her:
"Romance"
http://www.youtube.com/watch?v=mmx1r8AQNII
"Melody"
http://www.youtube.com/watch?v=DnJ1HAPi5Yo
"Melody - Salva Nos"
http://www.youtube.com/watch?v=DdGDNEMKFnI
"Le grand Retour"
http://www.youtube.com/watch?v=Jegn_XKxq9Q
They are my two favorite composers when it comes to OST's of anime. The best imo too.