I'm a deep sleeper and I can learn to sleep through any alarm that just beeps, so I wanted wake up to my music instead - dynamic, melodic, pleasant, and I can change it every day. Since all my favorite music is on my computer, I can pick the most pleasant sound to wake up to (Jolie Holland singing "Sascha", or the opening to a Toots and the Maytals concert, or U2 singing "Beautiful Day". I still sleep through the Beatles' "Here comes the sun").
The fact that I can listen to my own music makes this wayyy better than a clock radio.
I've been using this since I was ~12 or so. That's a lot of mornings spent reliability-testing this alarm clock by waking up on time for school, work, etc., until the advent of the Sunshine Alarm Clock I built last year.
*nix users can apply this easily to xmms (I've done it, it works). Windows users, switch to a better operating system, or hang on to your seats and maybe you'll one day be able to script your OS. These directions are for Mac OS/iTunes users.