Contributed by B@rt.
The only practical way to use Blender as a screensaver is with a game simulation. In this mode, you can make Blender quit as soon as you touch your mouse or keyboard.
1) Create a Python script in Blender with the following content:
import sys
sys.exit()
2) Create an 'all keys' keyboard sensor and a 'Trigger on Movement' mouse sensor. Connect them both to the same Python controller. Any mouse or keyboard action will now immediately terminate Blender.
3) Enter the name of the Python script of step 1 in the Python controller box.
4) Next, you need a Windows screensaver that calls another application when it starts. The following freeware program (ScreenRun v1.2) does that, although I've had some problems with it under Windows 2000: https://kmcsonline.com/freeware.htm
5) Create a .bat file that starts Blender in full-screen mode (-W) and loads your screensaver file (modify this as needed). Here's an example:
c:\progra~1\blender\blender.exe -W c:\myFile.blend
6) Save your .blend files as an Auto Start file! You can toggle this mode in the Game menu.
7) Configure ScreenRun to call your .bat file when the screensaver is activated.
This should do it! Enjoy - I'm looking forward to the first Blender screensavers! :-)