Since everyone now uses TextSecure (no, really, you should switch too!), everything close to a TextSecure desktop client is not finished enough and I want to type messages from my computer (in the old SMS ages, I did this with MyPhoneExplorer), I decided to remote control my Android device.
The setup is straight forward (if you already have root privileges on your device):
* Install a VNC-Client for Windows (for example RealVNC)
* Install a VNC-Server for Android (for example droid VNC server)
* Go through the settings of the VNC-Server
For some reason I cannot connect from my Computer to the Phone, but "Reverse Connection" works like a charm (don't forget to start the VNC Viewer in listening mode ... as ... some friend of mine did).
Edit: And after a restart of my phone, the normal direction also works.