Make a CD of songs you liked as a kid for the kids in your life. Chances are these songs will be brand new to them but will have the same appeal to them as it did to you. This will go over best for younger kids who don't yet have ipods or very distinct tastes in music. Some of my favorites as a young kid that I remember were Purple People Eater by Sheb Wooley and the Happy Days Theme Song. Think about theme songs from your favorite shows as a kid or songs you sang in music class. If you don't know the name of a song, you can search the internet by typing in partial lyrics.
A great gift for a sibling or childhood friend would be a CD with the theme songs of all the shows and cartoons you watched together as a kid.
For a good friend since high school you could put together a top 10 of your graduation year or songs you remember dancing to at your prom.
For anyone, think about songs about the place they live or grew up. Think about songs about the state and region.
For your spouse how about a CD of love songs you remember from your dating years.
Here are more ideas that can be used for anyone: Songs from movies they love, songs that make you think of them, or songs about their profession (this won't work for everyone).
You get the idea. Have fun with it and be creative. You'll have a thoughtful gift that is sure to be appreciated.