Are you only clearing the cache or other data like cookies as well?

Try to delete the cache folder directly on the hard drive.
You can find the location of the cache folder on the about:cache page, open this page via the location bar like a web page.

I didn't ask how to delete the cache, I asked why is it crashing or hanging? I already know how to delete the cache.

Are you saying the cache cleared quickly for you in Firefox 21? For me, clearing the cache locks up Firefox for several minutes -- on the rare occasion that I do it... (I do allow Firefox the full 350MB it wants to use.)

I am saying that it hangs and/or crashes, in Firefox 22 when clearing the cache, and I was asking if there was a fix to this?

If Firefox detects that it crashed, it invalidates the cache and doesn't use its contents. If clearing the cache after a crash also causes a crash -- at a time when the cache is minimally used -- the files may be corrupted. Please see cor-el's message regarding physically deleting the files.

Thanks.

The cache shouldn't get corrupted under normal circumstances.
You may have security software causing this if it happens regularly.