I like a lot of different music - I have broad but still quite specific tastes. I also like discovering new music, so I've tried things like Paste Magazine with its (now monthly) CD of new music, and a brief subscription to eMusic (good service for indie music, but picking new songs to download each month got to feel like a chore).
But I just discovered what may be the best way yet to connect my specific tastes with the desire to hear familiar music and to also find new music that I'm likely to enjoy, Pandora.com. Pandora is an internet radio service (free/ad supported or subscription) with a very smart interface. It starts by asking you to name a favorite song or artist, and it creates a "radio station" based on this. The station starts out playing songs by the particular artist (some of my stations are John Mayer, Paul Simon, and Joni Mitchell).
But here's the genius part. They have categorized tens of thousands of songs by their musical and performance qualities, and by comparing your choices to this huge database, they find other music that you might like. This music is "similar" in deep and often surprising ways, and you can further tune the process by adding additional songs or artists that connect in your mind (e.g., I combined Paul McCartney and Elvis Costello in one station). Sometimes it's wrong, and you can simply say "I don't like this" to skip the song and enhance their profile of your tastes.
It's way cool, and they have recently added a new "backstage" feature that let's you instantly find more information on the song, artist, or album (and of course to quickly and conveniently buy from Amazon or iTunes - I've already bought a few great new songs that Pandora recommended). Their goal was to recreate the experience of discussing your musical interests with an unusally knowledgeable friend or record store employee, and I think they've pretty much nailed it.