You don't often get a really beautiful picture in an article on punctuation, but here's one:
Do you see the light-coloured comma on the comma's wing? The comma is a common European butterfly and I'm lucky enough to see them in my garden quite often in the summer.
Many many commenters have written about the importance of commas, so I won't go into all that here. The fact that something vaguely connected has been around since the 3rd century BC speaks for itself.
The first punctuation mark to be called a comma was dreamed up by Aristophanes of Byzantium, who needed a way to tell people how much breath they were going to need when reading the next bit of text on the page. To do this he bunged in a dot before the chunk of text in question. You could tell how much breath you needed by whether it was at the bottom, middle or top of the line. A short chunk of text was shown by a dot in the middle (hmm...well, I suppose it must have made sense to Aristophanes at the time) and this short bit of text was called, yes, a comma (the dot was called a media distinctio, though people later started applying the snappier name comma to the dot itself, no doubt infuriating pedants everywhere).
To sum up...
...oh, all right. I can't resist. Commas can be vital, as in the notice on this public convenience:
ELDERLY DISABLED PREGNANT CHILDREN
Ah well, never mind. That notice must have given a lot of people a lot of fun, mustn't it?
Thing To Use Today Unless It's A Lot More Fun Not To: comma. This word is Greek and means something cut off, or a short clause.