There are so many pieces said before that I agree with, no need for me to repeat all of them. few I didn't see at first glance and I absolutely adore are:
Giovanni Allevi - Back to Live
Ludovico Einaudi - In Un'altra vita
David Lanz - Lost in Paradise
Scott D. Davis - Lost in the horizon
And the album Simbiosis. It's a live recording of a Manuel Obregon playing the piano in the Costa Rican Rain Forrest.

So tell me, what's it like living in a constant haze of stupidity?

Calling all dawns by Christopher Tin

It is a cycle of 12 songs sung in 12 languages performed by 200 artists from all over the world. One of the most magnificient album I've ever heard.

Fairy Tale
Next to you

It's not anime-related but the music 'River Flows in You' always has a place in my heart. You could play it near me under any situation and I will always be in the mood to listen to it from start to end.