Here in the UK digital TV & radio has had a reasonably succesful take-up. DAB is the standard for digital radio. It's good, though, much like the early claims with CD's, not quite as good as the hype would have you believe ('crystal clear, no interference..") with some stations subject to burbling & fragmented output or worse a somewhat muddied sound when compared against the FM equivalent) but nevertheless a welcome addition to the world of radio. Prices have fallen over the past two years, however the more desirable radios feature the ability to time-shift radio & record onto digital memory but at a premium price. Now, I'm a big listener to radio but largely via the internet as the range is obviously way broader than our DAB radio allows. I'm currently listening to Radio Paradise, a California based online radio station available to anyone with an internet connection. It even goes out of it's way to support an optimised stream for people on dialup, rather than broadband (using 24k AAC+ format for you audio techies out there).
Like all things technology, there are many different formats all basically trying to offer the same thing.
MP3 - The internet music format, widely playable via I-Tunes, Windows media player, Quicktime, real player etc.It's fairly safe to say that if something is broadcast in mp3, you'll have something that can play it.
Real - Requiring real player in order to listen.
WMA (Windows media audio) - Microsofts audio player format for Windows only (mac users need Flip4mac).
Quicktime - Apple's media player available for PC & Mac,
And in rare cases, as is the case for Radio Paradise - AAC+ - a version of AAC, the format used by Apple's I-Tunes store that allows optimum quality at small file sizes.You'll need either winamp or the excellent VLC , both of which are free.
A very rare format is the oddly named ogg, plugins available for many players including quicktime, winamp & support built into vlc. Ogg is very rare but great quality. Sadly it seems to be almost like the betamax of sound formats & I doubt you'll run into it very often.

A great place to look for internet radio stations is:
Live365
Shoutcast
or the Radio section of i-Tunes.
A subscription service XM also gives you access to satelitte radio, popular in the US.
Those of you on dialup only should look for 24k AAC+ stations at Tuner2.com
Have a listen. Enjoy.