Wide angle lenses have a property called barrel distortion. Since they are trying to pull in a very wide amount of information into the lens, some of the information on the corners (coming in at the most extreme angles) gets distorted because the lens can't completely correct for the incident angle.
On the widest side, you have things like fisheye lenses which make no attempt to correct this or even utilize it to get a wider angle. This is what gives fisheye lenses their distinct look. On the flip side, higher end wide angle lenses reduce the amount of barrel distortion through larger and more complex optics, but come at a cost of price, size and weight.
It is actually possible to get barrel distortion on just about any focal length, but wide angle generally show it the most prominently as the difficulty in correcting depends entirely on how far off the center axis the light is coming from.
Note that there is also an element of perspective distortion. This can not be addressed by even the highest quality lenses. The reason for perspective distortion is simply that, even when projected perfectly to a rectangle, if a camera is pulling in information from far to the side, it will end up looking a bit funny to us since we are seeing things normally outside our range of vision projected on to a flat surface.