I just noticed XB Stream has been released. While I have not tried this yet, it looks like you can stream audio and text XML feeds to your Xbox 360. (Kind of like TVersity)  Let me know if you install this and if it works well.

Disclaimer: install and use at your own risk

Edit: Turns out that this application downloads something on the order of the 30-previous shows of the default podcasts upon install. This is not a good use of bandwidth and is killing some of the podcasters out there, since many folks won't listen to the older shows. I have contacted the author and asked him to change the way the application works. Until this is fixed, I can not recommend you install this application and have removed the link.

Update: The author has made a fix that resolves the 'downloading a ton of back podcasts' issue, and he recommends that you download the updated version here as soon as you can.