It's dorky as hell but I loved most of the music from the Japanese version of the Digimon series. Dejimon Adventure, Dejimon 02, Dejimon Tamers and Dejimon Frontier, though a couple songs from Savers were good too. It's mostly just pop-rock by two obscure Japanese artists but the songs really invoke a sense of adventure and possibility, of magic. And the melodies are so original too! Butter-fly, Target ~Red Zone~, The Biggest Dreamer, Fire, Innocent, Slash, etc. So many good songs. The Spanish/German versions of some of these songs were equally good. Particularly the German version of One Vision, I think it was called Ein Vision or something.
Of course there are other anime far more suited for an adult audience with a spectacular soundtrack but those are songs that will always mean something to me and are still enjoyable on a musical level.
X3 on FLCL though. That show would be nothing without the songs of the pillows.