First off, sorry I haven't been posting! I'll be able to post more now.

I think people cover their mouths to both dampen the sound and hide the contortion of the lips. It's the same reason people try really hard not to break down and wipe away the tears before they fall, except it's even more extreme because the contorted mouth means that the person is crying really hard. People just generally don't like to be seen or watched while they're crying.

It's definitely a social thing. Children don't cover their mouths when they cry. In fact, many children are not embarrassed at all about sobbing in public. So, it's a learned behavior that adults acquire.

People probably do think that the contorted lip looks unattractive. Or they feel it's a "private" thing, so they're hiding it. I'd much prefer it if they just kept their lips uncovered, though!!!

I think Carrotcake is pretty much spot on - I asked my wife about why the hand goes to the mouth when women start crying. Not that she is particular guilty of this, only when she is extremely upset and sobbing uncontrollably.
Then its because she is trying to limit the sound of her crying. Usually when she cries she is quite quiet - only her voice is wobbly so if she is not talking then there is not much sound. But if she completely breaks down and starts the "shoulder shuffle" as she calls it then the sobbing sounds become louder and louder and the hand is to try and suppress this.

She told me she is more embarrased about the sound of crying than the visual element. She will cover her mouth and allow tears to spill down her face in full view because that to her its less embarrasing!

Tears indicate you are crying - that's ok - sobbing and making a noise indicate that you have completely lost control - much more embarrassing.

Yeah, it's the loss of control that people are uncomfortable with. I don't necessarily feel unattractive if I'm with my parents or boyfriend, but if I'm in public, I definitely feel the urge to hide it. Usually, that means turning away, putting on sunglasses, etc. I don't cry in public often... I don't think I've ever actually sobbed in public.

I remember posting about this on the FetLife group.  My mouth is the area I least want other people to see when I'm crying (if it contorts a lot, that is -- which isn't always the case, especially if it's just a few quick, gentle tears).  I don't know how I look, so I can't really describe it in any way (sorry, TorNorth!), but I think I probably look about average.  Although I don't know the reason, I've theorized that the reason I might be more self conscious about the look of the bottom half of my face is that while tears can happen for a variety of non-vulnerable reasons (like from cutting onions, for example), a distinctly downturned mouth seems to be more specific to crying.  But it may also be the case that I just happen to think that my emotionally wet eyes look better than my emotionally contorted face. 

Anyway, not that I normally do it myself, but as a guess, I would guess that women's hands fly up to their mouths primarily because they think it looks ugly and vulnerable (which of those things they find the worst probably depends on their personality).  And once a habit like that is formed, it might become so automatic that they don't even really realize that they do it.  I didn't even think about the muffling of sobs as a reason, but that's another good one...

I am actually thinking that guys are more likely to cover their eyes with their hands while women more likely to cover their mouths, but I could be totally wrong!  What do you guys think?  I am just thinking of some examples with men covering their eyes... even some from real life... yet I can't seem to think of a scene where a man is covering his mouth (although I'm sure they exist...)

Thanks for your input, Tearfreak92.  When I think of the definition of "crying", I do think of tears as being the main component of it, so it would make sense to me that men would want to hide their tears most of all -- they may regard it as the true breaking point, or the "evidence" that they are crying.

It might be that women are more OK with the concept of themselves crying and less OK with the concept of looking ugly, whereas men are more OK with the concept of looking ugly (in general, not just during crying!), and less OK with the concept of being caught with tears (it signals that they failed to contain their emotions).  Would make sense to me as a theory, anyway.