Gendou.com has a large collection of karaoke/instrumental songs from just about every anime out there, but some songs may have been taken down because of copyright issues. Other than that, you have a pretty good chance of finding the songs you want.
If the song you're looking for doesn't have a karaoke/instrumental version, you can always use the Center Pan Remover in audio editing programs like Audacity to try and take away the vocals, but that method isn't the most reliable.
