Vignetting adds a 'period' feel. I do a bit of shooting with actinic (violet-blue) light, which emulates pre-1890 orthochromatic film emulsions. Some vignetting enhances the Robber-Barons-era effect. Ah, and WHY was vignetting prevalent in that period? Because cheap traveling tintypists used cheap lenses to shoot multiple little pictures on one metal plate, to keep costs down, and those lenses didn't have an image circle sufficient to cover that place segment. Old and cheap, oh yes...
Vignetting has been used in portraiture for a long time, even in pre-photographic days, as a way to emphasize the subject. Many print mattes and mounts were (and still are) oval, or have rounded corners, or use devices at the corners to hold the prints, giving de-facto vignetting. Similarly, many portraits were (and are) shot with lenses or cheap filters that deliberately smear or fog the corners and edges, again to emphasize the subject. Some think of it as a 'romantic' effect. Form your own opinion.
A different form of vignetting comes from using a cheap wide-angle or fisheye adapter on a lens. Edges and corners are blurred, distorted, rather cruddy. These adapters were popular on early camcorders to give wide-angle or fishy effects, and because of the (low) quality and (mediocre) presentation of pre-HDTV video, the distortions didn't seem too objectionable. Put such an adapter on a FF or APS camera, or even on a better P&S, and the shortcomings are apparent. Such images CRY OUT for more forceful vignetting.
Or you can pretend it's a cheap Toy Camera effect. I cut out a piece of cardboard with a square opening and taped it over (and around) the fixed lens of an old 1mpx Sony DSC-P20 P&S. I get vignetting, light streaks, diffraction effects -- hey, it's almost as good as a Holga! And it cost absolutely nothing!
Notice how many times the word CHEAP appears above? That word is often associated with vignetting. Think about it.
EDIT:
Originally posted by Itai As Alain Briot said, the world does not get darker on the edges of our vision, so why would be shot that on photos?
Actually, the world DOES fade away at the edges of my vision, but that's because my eyes are deteriorating.