I selected three series that each composers has worked on- make note that they are by no means their best, or most significant works. I just selected the first ones that came to mind. They are sorted in order of preference.

Here are the composers I like:

• Joe Hisashi (Ghibli films, quite a few live action films)
• Michiru Oshima (The Tatami Galaxy, Sora no Woto, Little Witch Academia)
• Yoko Kanno (Wolf's Rain, Ghost in the Shell: SAC, Kids on the Slope, etc.)

Here are some composers I find okay (whipped together quickly, at best approximate order of preference):

• The massive composition team at MONACA (YuYuYu, Monogatari, Tasogare Otome x Amnesia)
• Kaoru Wada (Casshern Sins, Princess Tutu, InuYasha)
• Toshihiko Sahashi (Full Metal Panic, Gunslinger Girl, The Big O)
• Akira Senju (FMA: Brotherhood, Valvrave, Arete Hime)
• Yuuji Nomi (Sukitte ii na yo, Whisper of the Heart, Nichijou)
• Kenji Kawai (Gundam 00, Barakamon, Eden of the East)
• Naoiki Sato (Sword of the Stranger, Eureka Seven, Blood-C)
• I bundle these three together, for obvious reasons.
  • Kouhei Tanaka (Hyouka, One Piece, Diebuster)
  • Toshio Masuda (Ghost Hunt, Mushishi, Naruto)
  • Sagisu Shirou (Evangelion, Abenobashi Mahou Shoutengai, Bleach)
• Makoto Yoshimori (Baccano! + Durarara!!, Kuragehime, Natsume Yuujinchou)
• Iwasaki Taku (Gurren Lagann, Gatchaman Crowds, Noragami)
• Hajime Hyakkoku (SaeKano, K-On!, GJ-Bu)
• Masaru Yokoyama (Rolling Girls, Shigatsu wa Kimi no Uso, Joshiraku)

Here are the composers I am not particularly a big fan of:

• Kotaro Nakagawa (Planetes, Code Geass, Stella C3-Bu)
• Ryosuke Nakanishi (Highschool DxD, Hataraku Maou-sama!, Kuroko no Basuke)
• Susumu Hirasawa (Berserk, Paranoia Agent, Paprika)
• Ko Otani (Jinrui, Haibane Renmei, Another)
• Maiko Iuchi (Index + Railgun, Tokyo Ravens, Selector [...] WIXOSS)
• Tenmon (5 cm/sec, ef, Voices of a Distant Star)
• Sawano Hiroyuki (Attack on Titan, Kill la Kill, Aldnoah.Zero)
• Yuki Kaijura (Fate/Zero, Kara no Kyoukai, Madoka)

There's also Go Shiina, who did Kyousougiga, Gyo, and Majokko Shimai no Yoyo to Nene, but his work is all too similar for me to give a solid opinion on it. In line with other remarkable composers who were somewhat one-off: Choro Club (Aria), Kuricorder Quartet (Tsuritama), Suguru Matsutani (Usagi Drop, Nodame Cantabile), and Katsuhisa Hattori (Crest of the Stars).