How can I analyze and resolve a freezing menu bar? My menu bar is freezing up. Whenever I put my cursor near it, I get the spinning wheel of death (rainbow ball). I opened spotlight and it's stuck indexing. The progress bar isn't moving.  

I've tried rebooting, I've killed SystemUI and I've removed the SystemUI preference file but the problem persists.

How can I further analyze and resolve this issue?
I had the exact same problem for a while now and finally figured out how to fix it. My problem was directly related to 3-party menu icons though, FYI.

Open the utility called Activity Monitor and select the offending applications (they will be red and say "not responding") one at a time. Then click the upper leftmost button with the X in it and select Force Quit. That should remove the icon from the menu bar.