I've been using XBMC since the first Xbox was released, it was in fact my soul reason for owning an Xbox. Since then it's grown into a multi platform media player. It runs on Linux, Mac, Windows computers (there's even XBMCbuntu, a Ubuntu based distribution) as well as running on some embedded devices for example Apple Tv (boo!).
XBMC lets you play pretty much any media file from a local drive, network stream or remote share.
The Raspberry Pi performed pretty well, even though the software is still in it's release candidate testing phase.
I had some problems trying to install it first time round, the Raspbmc CDN was being DOSd so it wouldn't install via the interwebs. I downloaded a pre built image file and used dd to image the SD card.
It ships with plug-ins for the BBC iPlayer, 4OD, ITV player and some other video streaming services, the usual audio streams are also included.
Plain sailing after that. The video below depicts me mumbling and sitting too close to the monitor, holding my phone in one hand and driving XBMC via the mouse in my other hand.
Full screen available: