The big one for me is the ability to remotely display windows. And VNC doesn't count, as that's not really the same thing. There are a number of other things as well. Extensibility, platform agnosticism, avoidance of integration into the OS, etc.

I will freely admit that there are a huge number of problems with X, from inconsistency (Xaw, Xm, Gtk, etc.) to usability (xwd | xpr), ugliness (bitmap-only font renderers) and any number of other things. But as far as being able to actually do just about anything, nothing else comes close (except, possibly, NeWS, which I haven't used in so long, I couldn't make a reasonable comparison).