Tech/culture connector Scott Beale turned me on to Muxtape, a super-simple site that streams a list of MP3s via the browser. Playlists you create get their own simple URLs and the interface for controlling the stream is plain and intuitive: Click a track to play it. Click again to pause.
You have to upload MP3s to the site to create your playlists, though, and while the interface for doing so is simple, it's rather a drag. There's no bulk uploader. You have to select each file from your disk and upload it individually.
Unfortunately, the site is Napster-esque in its disregard of digital rights. You can upload any MP3 file to the service and distribute the playlist URL far and wide. I strongly doubt the site's legal notice on the upload page is enough to shield the service and its users from the law: "By uploading a song you agree that you have permission to let Muxtape use it."
That's a shame, because it really is a nice service. To use Muxtape is to replicate very well the old experience of making a cassette mix tape (if you're old enough to remember that). The differences will kill the site, though: your Muxtape site can be instantly played by millions of people, and the audio is a perfect digital copy of what you upload.