Today, Microsoft has rolled out the web version of their Xbox Video app. The site/service mirrors the look and feel of the Windows 8.1 app pretty closely. The site gives you access to the videos you've already purchased located in a "Collection" area. Amazon, which I use quite a bit more than Xbox Video, stores your purchased items in a "Video Library." Different names, same effect.
Using the web site you can purchase or rent new videos (movies or TV), which are then available to stream through your web browser using Silverlight, or on the many other devices you own that are connected to Xbox Video. So, for me, for example, I can rent a family movie for the evening while I'm thinking about it, and then just power on our Xbox 360 in the family room when ready.
Search works well, too, allowing you to filter by a multitude of criteria, including actor, title, director, etc., etc.
The site can be access by hitting the http://video.xbox.com/ link.