There's no shame because I'm not affiliated with this product, but also because I have no shame.
Pandora Basically, it's an internet streaming radio site.
You give it one or more artists/songs you like as a starting point, and it plays stuff it decides you might like based on what you picked. As you tell it which of those songs you do and don't like, it adjusts the picks accordingly. I'm pretty happy with it so far -- the free version of the service supposedly has ads, but I've listened to about 20 hours worth of music so far without hearing any. If you like genres of music that don't get normal radio play, it's not a bad way to be exposed to some artists in that genre that you might not have heard.
Launch does something similar to this, but will play you songs from their featured artists/advertisers, so you'll be listening to like classical jazz and they'll decide that Britney Spears somehow fits your preference and play it for you. I haven't had problems of that kind with Pandora yet.
One piece of advice if you check it out -- for best results, create a radio station for each genre that you want to listen to. If you tell if you like Miles Davis, Bree Sharp, Bad Religion, Mephiskapheles, and showtunes (or whatever), you're going to get some weird results as it tries to find a common thread there.