Actually, even games that natively support widescreen resolutions will distort the picture in some way. Every single game that I've seen so far has either done linear stretching, panoramic stretching, or clipping to fit the picture onto the screen. Then you have the fact that for a given diagonal, the closer the screen is to square, the more surface area you'll get. And of course most web pages are designed for 4:3/5:4 resolutions, which in many cases results in ugly browsing. It's also worth noting that not only is it quite possible to put two windows side by side on a 4:3 screen, doing so is rarely necessary unless you are actually able to read two things at once.
Pretty long list of disadvantages, isn't it? Well, I'll now start to argue against them, if you don't mind. Lots of people don't notice picture distortion or clipping in games.. the former is easy enough to get used to if you're not big on picture quality, and most people don't use the extreme top and bottom of their screens often enough to care about cropping. The surface area advantage of widescreens isn't that big of a deal, and they're close enough to begin with. There are conceivable scenarios in which one would want to put two unusually wide documents side by side to compare them.
I'll also say that I love widescreen monitors for DVDs, for obvious reasons. Just saying that 4:3 screens are in fact generally better for games, but how much better they are will vary from person to person.