Some shots, like vehicle pursuits or crowd turmoil, require some camera vibration to look authentic. However the majority of situations, especially when shooting from a distance, really benefit from shooting with stability.
To achieve a stable image simply requires some ingenuity in using the surroundings for support or the purchase of a tripod.
Shooting with a small focal distance is also helpful to minimize vibration.
Software available today can stabilize the image in post-production to a point, but bear in mind it crops the edges of the video.