Found a decent guide for ripping your DVDs onto your Media Center PC to playback through the 360. The guide is heavy on DVD-ripping and light on 360 Media Center extender integration, but provides the necessary steps to to get the video files prepared. The guide warns, "This how-to presumes that you have the XBOX 360 and the Media Center PC configured to share media files before you start" and concludes, "go to the Media Center menu (on either your XBOX 360 or your MCE box) and select My Videos. You should see your new file in the folder with the rest of your video files."
Something tells me if you're able to set up your Media Center PC to share files with your Xbox 360, you probably know the procedure to rip DVDs already. If not, consider this a primer, or inspiration to get that DVD collection ripped onto an enormous hard drive ready to be streamed to your 360 at your whim.