While anime can be absolutely stunning to look at, there's obviously a lot more to entice you. There's storylines, dialog and so much more. For me, one of the biggest elements to any great anime has to be a fantastic soundtrack. I feel the same way about video games, and I've found that both mediums offer up some amazing auditory experiences.
You know music is good when not understanding the lyrics doesn't even matter! The soundtrack in FLCL is absolutely outstanding, and it turned me onto a wonderful band called The Pillows. The track above is found in FLCL, but it's just one example of how great this band is. I picked up the entire soundtrack collection for FLCL to begin with, but now I own a few separate albums from The Pillows as well. Unfortunately, I always seem to miss out on their band tours when they hit the states.
Now Death Note is an anime series that deserves a entire collection of posts, but that's for another day. For now, I just have to say how ridiculously good the entire soundtrack is. I'm sure it's even more enjoyable to those that have seen the series, since you'll tie certain moments in the anime to the music itself. With that said, you can definitely enjoy the music on its own. Just the other day I had a friend comment on this music to say how great it was, and they didn't even know what Death Note was.
Any self-respecting anime usually has a great theme song to go along with it as well. Haibane Renmei is no exception. This song is completely different from the ones above, but it's beautiful nonetheless. These are tunes that can be appreciated by anyone, no matter their knowledge of anime.
Perhaps anime music is the perfect gateway to anime itself! If you're trying to get a friend in on anime, why not let them hear some tunes from your favorite feature? When they ask where the content comes from, show them instead of telling them!