As to them keeping you drier, yes they do in situations where dryness stands a chance of prevailing. But otherwise once you are wet you are wet. Once truly wet I'm not sure the degree of wetness makes much odds. But I am sure the amount of crap sprayed over your gear, and your bike is important.
I sense there is a bit too much religion in mudguard debates for my liking so I'll keep this brief!
My experience of riding in sustained heavy rain and on wet roads on three significant occasions over the last year is that my mudguards have kept me dry and comfortable while those riding with me without mudguards have been wet, dirty, miserable and very cold! While I obviously prefer it to be dry, unlike many people who don't use mudguards, I don't particularly dislike riding in rain.
As is often the case, User482 explains it most clearly above and McShroom provides additional colour! I disagree with Greg's statement because mudguards prevent parts of you from getting wet which do not tend to get wet directly from the rain.
The longer the ride, the more important it is to stay dry. There is an article by an American mag which tried to do some analysis on correlations between bike set-up and success in completing PBP. They found that the biggest single predictor of whether someone had to abandon the, famously wet, 2007 PBP was whether they had mudguards or not.
It's personal choice but I do feel a little bit uncomfortable when beginners are coerced to dispense with mudguards. Obviously, badly fitted bike parts are a hazard but mudguards, like wheels, tyres, chains, gears and brakes, can be fitted properly before the ride rather than having to be ripped off. You don't need mudguards if you live in California, Southern France or Italy but not using them in Northern Europe is putting fashion above practicality.