Windows – Remote desktop connection without locking the remote computer

Your answer is:

mstsc /console

This connects to the console session (which is what's being displayed at the local console, aka the local monitor).

Quit Remote Desktop client first, then run the command above from the commandline. There will probably be no visible indication you're running MSTSC any differently, but it will work.

If you log in as the same user as the already logged-in user, then you will take over their session. However, the user sitting in front of the PC will be disconnected from the session and see the login screen. If the user logs in again, then you will be disconnected and the user continued from where you left off. At no point is the user's session terminated - the programs continue running.

You can use Windows Remote Assistance, which is based on the same technology as remote desktop. It allows you to view and optionally control the current user's session without them logging off.

Another alternative is Remote Administrator, which I used heavily before remote desktop became widely available.