What is a good X application I can use to test the X server on Solaris?

xset -q > /dev/null

I found this over at https://stackoverflow.com/questions/637005/x-server-running (in response to a somewhat misleadingly worded question).

• quick
• usable in scripts
• quiet if OK; diagnostic for problem on stderr

I am sorry, I failed to mention that I was using Oracle Solaris 11.

In this release, none of these come installed by default (used the text installer). You have to install them using the package manager. To find which package contains the application you want use pkg search:

pkg search xeyes 

I used the compatibility/packages/SUNWxwplt package and it installed xterm and xeyes to /usr/bin.

You may want to expand your environment variable PATH to directory /usr/openwin/bin:

 PATH=$PATH:/usr/openwin/bin

That's (for historic reasons) where X11 applications reside on Solaris. There you may find xterm, xclock and many other base clients for X11.