I initially tried using PS3 Media Server, but that seems to be quite unstable. The server will often crash when streaming audio, and my initial attempts to stream video didn't go well at all.
I'm also investigating Rivet (free but discontinued), MediaLink (USD $20), and Playback (USD $12 on sale; $21 normally). I've not tried the latter yet, but the other two seem to work well enough. However, they don't allow me to stream purchased video content.
Another possibility is getting an Apple TV. It certainly seems to have a pretty slick UI, but I still need to investigate whether this will play nicely with my A/V receiver. It only has one free optical audio port, which is currently in use, and doesn't support HDMI at all unfortunately. It does have a spare coax digital in that I may be able to use. Is it possible to get a cable or adapter to allow me to go from optical audio to coax?