I think it depends on the place, and the type of signature. Putting your own name there, wether it's your screenname or your real name, is sort of like signing it. It means you really stand for what you wrote.
On one forum I frequent most people belong to the same organisation, so most people have a signature with their full name, their position, the sub-organisation they belong to, and contact details.
I've also seen some rather succesful disclaimers.
A few people also use it to dissuade misunderstandings, by trying to bridge one of the faults of internet communication. Mood is rarely readily apparent, so signing your post with "Jokingly, Silver", or similar could theoretically help.
Then again, on a lot of other forums it's just a lot of nonsense. I think that, if limited in size, it can be a nice thing. Makes it more personal. Just remove all the silly pictures, and limit it to one sentence, or one set of contact details, or something. It's a useful tool often used for annoying purposes.