Fans of Attack on Titan or L'abaresque Sindria should check out Shiro Sagisu's superior work on Rebuild of Evangelion. This is one of the best pieces to come out of Japan - https://youtu.be/EYms5h0HnMo
His Black Bullet soundtracks are also good, particularly the first one.
Almost all of Yoko Kanno's work is worth tracking down. Here's an obscure piece I bet no one knows - Exaelitus Do you know why you don't know it? Because this is from a commercial for a Lexus SUV or something (Toyota Exaelitus in Japan?). Ridiculous. It should be from Escaflowne or Macross Frontier.
The Ar Tonelico games produced a surprising amount of good music - METHOD_REPLEKIA/.
EXEC_PAJA/.#Orica extracting
All the songs are sang in the language of Hymmnos, which is itself fascinating.
The Record of Lodoss War OVA soundtracks are great. Record of Lodoss War is ancient now, but basically it is what you'd get if you took "The Lord of the Rings" and made it good.
Record of Lodoss War - Honoo no Lagrima
Adesso e Fortuna
There is a longer version of Adesso e Fortuna out there, and versions in other languages. I prefer the longer Japanese version. Video is from a game, not the anime, which is gorgeous. It doesn't have all the computer coloring and shaky cam you see today, but the drawings are far more detailed than you usually see in anime, and the character designs are second to none.
There was a not-terribly-good TV series that produced a few good songs, I believe Yoko Kanno did the good ones or was involved to some degree -
Kiseki no Umi - the Japanese version is sung by Maaya Sakamoto, who voiced Hitomi in Escaflowne.
Hikari no Suashi
There's also Mistrel's Memory of Lodoss, a very obscure soundtrack. This is composed by Masumi Ito, who IIRC is better known for the opening to Azumanga Daioh.
Here's the first track -
Voice of Elf
The Azumanga Daioh opening is good too, if insane -
Azumanga Daioh - Opening Song
Revolutionary Girl Utena had an amazing soundtrack.
I'll also 2nd the Tenchi soundtracks.
Cinema Symphony - Ghost In The Shell OST <- Ghost in the Shell played live.
The soundtrack for Bokusatsu Tenshi Dokuro-chan has some good tracks -
Dokuro-chan Opening
dokuro-chan ending 2 HD
Well that's it for now.