I mostly use X11 for somewhat more obscure things, like nessus, the vulnerability scanner. I'm taking an info security course, though, so that's a bit of a special case...
The real killer though is if you have ssh access to a Linux computer (like I have access to a couple at school), then you can 'ssh -X
me@the.linux.box' from an xterm window, then you can run graphical apps on the Linux machine and have the display on your own screen.