How can I analyze and resolve a freezing menu bar?
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.