It is inevitable that if you watch anime, you will like J-Pop. The opening and ending songs of each anime are often well-composed pieces of music by established Japanese artists or composers. Also, what sets anime apart from western television series is that the opening and ending songs may change during, or between seasons. Therefore with series like Naruto and Bleach with hundreds of episodes and numerous seasons, you get to hear many catchy tunes that you might want to put on your mp3. The problem is often that they are not easy to find on conventional sites; and if you do not know japanese, they may be even harder to type in search fields.
Luckily, some people have set their mission to let other than Japanese people listen to Japanese music! An example is http://nipponmedia.net/ where the signature Kurosaki often posts nice information, covers and links to downloadable Japanese and Korean songs and albums. This is where I for instance, got hold of the latest songs for Bleach and Naruto Shippuuden (watch the below video).
Long Shot Party – Distance
The songs you hear in anime series are often cut versions to fit the opening or ending of the anime. As such, the original versions of the songs can sound differently from what you heard in the anime.
Questions on legal issues at Nipponmedia can be found here: http://nipponmedia.net/about/
For Bleach songs check: http://www.bleachexile.com/multimedia/bleach-music-downloads/ (free membership)
Japanese music on Bittorrent: http://nipponsei.minglong.org/