at first I thought it was the whole "mirror" thing. people grow up looking at their self in a mirror and unless your camera has a setting to reverse (mirror) the image than you would look weird in a webcam.
if lot's of people say a webcam makes you look weird/different try moving it different heights. most webcams sit on top of a monitor and it might just be a very odd angle. perhaps you need to move the webcam or sit on top of a few books so it's right in front of your face rather than above it.
Combination of bad and/or unnatural lighting, cheap webcams, and possibly bad software.
Simply put, the lighting thing usually is because when you're in front of the webcam, you're probably in a room that is low light, and therefore the blue of the screen is giving you a ghoulish disposition, or the room is too bright and you're backlit, or a combination of both. Also, beyond that, a good camera and video software could help with that. Though that usually means spending more.
why worry about what you look on webcam? I would be worried what I look like in real life. isn't that more important. maybe its the webcam you have got. its not got very high definition or many pixels on it.