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, HERO3, HERO3+, and HERO4 camera, you also have the option at 1080p to switch to a medium (127 degrees) or narrow (90 degrees) FOV. The HERO3 White Edition camera only films video and takes photos in the WIDE FOV.
If you want to get rid of the barrel distortion or "fisheye" look of your GoPro videos, you can use GoPro Studio to import the footage and check the "Remove Fisheye" checkbox. This will allow you to export the videos without a barrel distortion or "fisheye" look.