Cats' eyes will "tear" or water for a number of reasons, but they are all medical, not emotional. They include eye irritation from a speck of dust, a scratch from another cat, or allergy. They also include contagious diseases, such as upper respiratory infections. Clogged tear ducts (believe it or not) can also result in tearing.
While cats certainly do have emotions such as grieving or depression, they express them in different ways other than crying (lethargy, withdrawal, disinterest in food are a few examples.)
This is just my opinion, of course. I find this question so interesting that I'm going to post it in my FAQ section, and wait to see if some expert will refute it with scientific data.
UPDATE:
Several years after writing this FAQ, I still have not seen any scientific proof that cats cry in an emotional way. However, judging by the anecdotal comments inspired by the question, I certainly am willing to reconsider my views.
