Chances are that if you shoot hand-held without any sort of stabilizer, as many of us do, you have had to deal with shaky footage before and how to avoid it. Nothing makes video look more amaturish than shaky footage. Stable video is one of the tings we look for when assesing quality in our everyday viewing.
If you are just shooting your cat looking cute on the couch you can probably get away with it, but if you are doing anything else, you'll want to make sure that your footage is stable. As video has become more and more ubiqodous, particularly on the web, viewers are exposed more and more to quality content and therefore come to expect certain norms when they watch video -- such as clear audio nad a stable image. If your video is shaky, chances are people are going to turn it off pretty quickly.
Here are some tips from Peter McKinnon on how to get stable video when you are shooting hand-held: