If you do a lot of driving in deep mud, pay and play hats that sort of thing, then they will forever trap stones and are probably best left off, however...
For a primarily road going vehicle they do a couple of important jobs. They keep dirt off the brake discs, this is particularly important on the rears, when mine were missing I found brake pad life reduced considerably. Secondly they prevent a lot of water and road spray from getting on the disc, my front ones are off at the moment and I have noticed that on wet roads after being in someone's spray trail for a while the first press of the brakes is less effective as the pads clear the water, they work fine after that but if that first press is important it could be an interesting moment! No such problems when they were fitted and then will go back on when I get around to it.
Basically they do serve a purpose, and unless you are operating in the sort of conditions that cause the problems with them I would leave them on.