The reason GoPro videos have a slight fish-eye effect, is due to the wide angle lens on the camera. It's actually called a barrel distortion, which is a result of having the 170 degree lens. This curve/barrel distortion allows for the 170 degree ultra wide angle shots that GoPro is known for.
You can slightly reduce this effect on the HD HERO Original camera by filming in 1080p (30 FPS) mode, which brings the Field Of View (FOV) down to 127 degrees. With the HD HERO2 camera, you also have the option at 1080p to switch to a medium (127 degrees) or narrow (90 degrees) FOV.