When you Remote Desktop to a Windows XP Professional computer, you always connect to the console session. This is the default for Remote Desktop to Windows XP Professional. When you remote desktop to a Windows Server 2003 computer, the default is to start a new session. But you can easily connect to the console session of a Windows Server 2003 computer using the /console switch. This is nice because at work I run Windows Server 2003 as my operating system. Then when I go home and Remote Desktop to my work computer, I can get to all of my currently running applications without having to start them up again.
To start Remote Desktop in console mode, run this from the command-line:
UPDATE (8/15/2008): Windows Vista remote desktop client does not use the /console switch anymore. It now uses a different switch (/admin) to get to the console session on the server (thanks Drewskie):