I have two internet radios; a Noxon iRadio and a Sangean WFR-20. The radios work independently of a computer, basically looking like a sometimes rather bulky transistor radio or table radio.

Hmmm ... freely available; more about that later ...
However, at the moment, the latest firmware is getting rather long in the tooth, although there is a beta-version available, but I can't get it to upload into the Noxon. One of the advantages of the Noxon is that it's a nPnP device and it can have some of its features controled via its own internal web interface. It uses the vTuner portal for access. vTuner is a pretty basic service with no user forum or similar available. It is also not able to access stations broadcasting in WMA, a problem if you like nice quality on the BBC. On the other hand vTuner has been pretty reliable.

Unfortunately the Sangean does not use nPnP, although the latest beta-firmware is working in that direction.
The Sangean uses reciva.com as a portal. Stuff like favourites, streams and podcasts are controlled via the portal. Reciva also has the benefit of a lively support forum, although the forum software is pretty clunky and slow. Beta-firmware is available via the forums.
I also started iRadioForum.net for general internet radio chat and support. It's a bit slow taking off ... but who knows?
Internet radio does face some challenges though, in particular, geo-blocking and station flash-players.
Geo-blocking is internet radio broadcasters' response to rather dated copyright laws, sometimes just irritating - ie: BBC Radio 5 Live Premier football match commentaries blocked - but largely just plain restricting. Another problem is that radio stations will only play via a specially developed flash player application and stream, thus unavailable to internet radio devices and frequently associated with geo-blocking too. In other words, radio stations, and particularly US stations are determined to chain us to our computers.
Hopefully there will be a way around this.