Piece of cake. There are many solutions. Netgear do a jukebox that will play your collection of Rolf Harris around the house. If memory serves rght, it is the MP-101.
Failing that, there are modulators that will plug into your device and if you set a corresponding frequency into a radio, it will play through there - and no need for a router, either.
Internet radio is a bit different though. Many of the staions you might like do not transmit streaming MP3 as you might like. I have acquired a PDA with an internet radio function, which I wanted to listen to the shipping forecast on Radio4. I don't quite work that way. Many stations are streamed for either Media Player or RealPlayer, but not an .M3U format which is what you apparently need for "naked" MP3. I am still learning, but aren't we all...
Conan