There are a fair amount of anime soundtracks available on iTunes and Amazon, but it's not particularly expansive. Here's one I can slightly recommend, it's two legendary anime songs in one little package!
Ai O Torimodose - EP by crystal king - Download Ai O Torimodose - EP on iTunes
The thing keeping it from being a hearty recommendation is that while it is the original singer of those songs, they are not the original versions of those songs used in the anime. So they're a little different.

If you just want to listen to 'anime music' or Jpop in general, there are a number of internet radio stations dedicated to just that. The problem is you don't get any real control over what they play, but the upside is that you might discover something new. Here are a couple, but if you just Google something like 'anime radio' or 'jpop radio', or even get WinAmp and search their ShoutCASTS, you'll find several of them.
Listen to ArmiTunes (Dynamic) - Armitage's Dimension
AnimeNfo Radio V2 :: Your BEST source for Anime and Japanese music!
Kawaii-Radio