TwitSaver Twitter Screensaver
Of all the currently released Twitter screensavers Twitsaver is definitely one of the more interesting ones. Unlike Twitter Screensavers like Flitter or TwittEarth that concentrate on the locations and messages that are sent by Twitter users, Twitsaver does concentrate on images that get referenced by Twitter users in their messages.
The homepage does not contain information about the criteria that are applied by the Twitter screensaver. The screensaver will display an image once it gets turned on. The major part of the screen is reserved for the image while a smaller strip on the bottom is reserved for the name of the Twitter user and the message send by that user.
Images are rotated every 30 seconds automatically. This basically means that a new image and message are displayed every 30 seconds while the Twitter screensaver is running. The screensaver requires an Internet connection to pull the data from Twitter.
The major drawback of Twitsaver is that it does not offer customizations. It is not possible to change the frequency or specify certain Twitter users that should be used exclusively.
Update: The Twitter Screensaver is no longer available, the web page it was hosted on is throwing a 404 not found error message when you try to open it. It is therefore safe to assume that the Twitsaver project is dead, which may have something to do with recent Twitter API changes.
I'm not aware of a comparable program at the moment. Your best bet is to use one of the two Twitter screensavers listed above, which both are still available and it seems functioning at the time of writing this update. Keep in mind though that this may change in the future as well. For now though, they are your best bet when it comes to displaying Twitter contents on a screensaver in Windows.