You will notice that there is a trick involving buying Japanese gift cards from a middle-man like Japan Codes and then creating an iTunes Japan or Amazon Japan account, BOTH OF WHICH ARE ILLEGAL if you don't live in Japan because they require that you have a valid address in Japan. It tells you ways to obtain Japanese music outside of Japan both physically and digitally. Other than legally purchasing from the small library of anime songs available in your own country digitally from iTunes/Amazon MP3, (I know this defeats the purpose of your question of digitally obtaining anime music, but) unfortunately the only other option is to purchase physical CD's from various vendors like Amazon, CDJapan or some other CD distributor. If you don't live in Japan, as the above link alludes to, then it is very difficult to truly legally obtain anime music via download.

Joe Hisaishi's complete OSTs for a couple of Miyazaki films including Spirited Away, Castle in the Sky and Princess Mononoke (iTunes only).

Hiroyuki Sawano's OST for Attack on Titan ( nothing for Aldnoah Zero though) and Linked Horizon's 'Guren no Yumiya' and 'Jiyuu no Tsubasa'.

Most of Fairy Tail's opening/ending songs ( NOT the OST though, unfortunately).

LiSA's 'Crossing Field', 'Shirushi', Eir Aoi's 'Innocence', 'Ignite' and a couple of other opening/ending songs from Sword Art Online 1 / 2.

Yui's 'Again' from Fullmetal Alchemist Brotherhood.Amazon MP3/iTunes Stores (but the trend seems to be that there is mainly J-Pop opening/ending songs, and very little instrumental OSTs): Here are couple examples that I have found in either, or both the U.S. However, there is a small amount of anime music you can find in a non-Japan iTunes/Amazon MP3 store. Note that I emphasize the JAPAN you will likely NOT be able to find what you're looking for in an Amazon MP3 or iTunes store for a different country.ДЄlthough it pertains to the United States in particular, this link more or less explains the gist of why that is so. If you live in Japan, then you can find pretty much any anime soundtrack OST/opening/ending/insert song in the Amazon MP3 JAPAN store or if not there, the iTunes JAPAN store for purchase. I don't refer to others distributors because whatever they offer will likely be available in either, or both, iTunes or Amazon MP3. Note: I only mention iTunes/Amazon MP3 because they are the largest distributors of digital music for purchase. I've picked the links that will land you at appropriate places. The prices can sometimes be very well placed. If you're American, you should know about Right Stuf Anime and The Anime Corner Store.ДЇinally, I recommended you try the mighty Jungle. Also, it may be that the above mentioned HMV only lets Japanese people buy.

If you're a resident of Japan, check the comment by another user. If you can read Japanese, HMV Online is a Japanese website that gives good deals but may be limited in offers and variety of payment. But that's not what you asked for, so sorry. If you feel adventurous, there's more! Like Frozen's Japanese (or was that Korean) version and K-pop songs, etc. Here you can find exclusive and good amount of foundational soundtracks. I buy things from there as it accepts my currency too (INR). I'm giving you the link that points to its English anime page. However, here's the catch: they focus more on offbeat and non-mainstream-anime related things.ДЇor some miscellaneous and also filterable (like in English, Bestsellers, Great Deals, New Releases), I recommend YESASIA. There's a Japanese website, CDJapan, from where you can order CDs.

Anime soundtrack download