I have always been into still photography more than video, but since I got a video-capable DSLR a few years ago I have tried to shoot video clips when the opportunity permits. I have created a video from a variety of clips showing deer, foxes, badgers, water voles and more. I will also give a few thoughts on techniques.
Why use a DSLR for this rather than a dedicated video camera, which after all are nowadays relatively small and cheap? Well, partly because I do not own one, and try to carry around as little gear as possible (not that you would think that, to look at how much I often carry). Also if you are using the same camera and lens for both, you can switch between stills and video in a second, rather than having to swap equipment. You can get attractive out of focus backgrounds due to the larger sensor size of a DSLR, especially when combined with a 'fast' (large aperture) lens and if you are shooting from the subject's level.
Why use a DSLR for this rather than a dedicated video camera, which after all are nowadays relatively small and cheap? Well, partly because I do not own one, and try to carry around as little gear as possible (not that you would think that, to look at how much I often carry). Also if you are using the same camera and lens for both, you can switch between stills and video in a second, rather than having to swap equipment. You can get attractive out of focus backgrounds due to the larger sensor size of a DSLR, especially when combined with a 'fast' (large aperture) lens and if you are shooting from the subject's level.