I remote into servers... a lot. And by default, Server 2003 only allows two concurrent connections at any given time. There are plenty of other posts on how to configure this, but it doesn't do any good if you can't get to the server.
Fortunately, there is a brute force way to bypass this.
If you receive the error "The terminal server has exceeded the maximum number of allowed connections", simply launch remote desktop from the command line as such:
mstsc -v:0.0.0.0 /f -console
Where 0.0.0.0 is the IP address or server name of the server you want to remote into.
If that doesn't work, another option is to go into admin mode.
mstsc /admin
And remote in like normal.
You can also use this nice little tool to find out who is logged in:
qwinsta /server:[servername]