I think when you laugh you're giving the other person (the one who did the embarrassing thing) the opportunity to laugh it off instead of being all shy and ashamed about it.

I've wittnessed several situations where someone had an embarrassing moment and nobody laughed. They just sort of looked at him/her. I think that's a lot more embarrassing and awkward than when everybody laughs at/with you.

it's funny, also it helps to distract. Many times I have had embarrasing moments on the street, jejejejeje.

It's funny because it's so relatable. We've all been in their shoes before and know exactly how they feel - which makes it hilarious. I actually laugh more when it's me that's done something really stupid.

I think most of the time it's nervous laughter rather than people finding it funny.
Nervous laughter is the body' s response to a distressing situation. I think a lot of people experience nervous laughter when they are overwhelmed, perhaps if they don't laugh they would cry instead. Laughing induces endorphins (chemicals the brain releases to make you feel better), so perhaps it's the brains way of calming someone down in a stress situation.

I also think some people do laugh intentionally to try and lighten the situation. When someone does something embarrassing it's often awkward for the person involved and the people around him/her. Laughing can take the seriousness and awkwardness out of the situation.

I'm sure there are tons of reasons :)

I think it depends on point of views. Who says that singing alone in the train a bit louder is a sin?? maybe the only problem is broadening one's horizons and look at things in a different way, an everyday exercise that all of us should do.