A video is a good idea if - and only if - it can show the subject better than text or static images could. A video for its own sake is annoying and counter-productive.
Some examples: how to make a loaf of bread; how to change the brake pads on your bike; how to clean the inside of a computer: those are all useful subjects for a video. But if you want to explain, for example, how to code a webpage in HTML, or whether it's safe to eat out-of-date food, a video is a waste of time and effort. These are things you can explain much better with text. Particularly annoying is a video of a person talking straight to the camera, when what he is saying could just as easily be presented in writing.
The problem with a video is that the visitor might have to set aside time to watch it (so that it won't disturb those around him); the video might not be compatible with his system (it might not support Flash, for instance); or he might not have enough bandwidth to watch (if he is using a mobile device with a restricted data plan perhaps). With a straight page of text, you can read it at any time, in any order; you can easily jump around, and focus on specific bits of information; you can copy and paste it, print it, search it, and run it through a translator. Those things are harder to do with a video.
So, yes: use a video if it really enhances the page or communicates the message. Not otherwise.