Only as a comedic undertone with tissues that the villain just so happens to have on-hand at the time...
I find whenever a villain does cry, in general, it's suppose to be sympathetic... But, then again, whenever it does happen that way, I usually do not have any sympathy for said villain, thus causing others to call me a cold-hearted[footnote]Contradictory, considering that one quiz I took some time ago...[/footnote] bastard for not caring...
Look, if it can be pulled off correctly, then fine... otherwise, don't do it unless it's something that that particular villain would do in that given situation...
Edit: Manual spell-checking late into the night...