How to run a GUI program as a different user (Debian)?

First off, don't use sudo or su to change users to run a graphical process, or you're liable to have problems down the line (~/.ICEauthority changing owner is a notable issue). Instead, create a shortcut that uses the following command:

gksu -u [user] command

gksu launches a graphical prompt for the user's password, and upon entering the correct password, launch the application as the user specified.

my own solution involves ssh. when I want to run <command> under a different user <login>, I do this:

ssh -CY <login>@0 <command>

yes, I do need a ssh server in place and I do need to either enter the other user password or to have my own public key in ~<login>/.ssh/authorized_keys2. and I cannot close the terminal from which I gave the command.