Especially concerned to be a problem for DSLR’s, the image shakiness can rapidly degrade overall image quality and the feeling of professionalism (if that is desired). The so called form-factor (term describing the physical properties of an imaging device) of the DSLR’s are not really suitable for handheld shooting. The DSLR’s are small and lightweight and the way they are operated requires user to keep the camera relatively up and with postures where muscles are prone to tension, which will (eventually more due to muscle-exhaustion) introduce small vibration to the image. More heavy camera body would absorb some of that vibration, and also cameras with better form-factors including handles or shoulder pads, which would reduce the trembliness significantly. All sorts of rigs can be built for the DSLR’s to improve it’s form-factor, though more cheaper options to counteract the restrictions of the form-factor are available. A tripod is as suitable for use with photography as for videography, and not just static shot but for moving shots also. Tripod allows better control for the shoot, and can even be rigged to a small stabilization device. The trick is to find the balance point where the tripod is held in hand from the point where there is equal weight upwards and downwards from the operators hand. This is the basis for Steadycam systems, and can significantly lower the amount of the undesirable shakiness.
Though solutions have been made for this problem. Many softwares offer in-package stabilization tools, and many plug-ins are available. What stabilization tool does, it analyzes the footage in 3D-space using parallax, creating a 3D-representation of the camera movement, then by usually scaling the image, offsetting the image center to stabilize the image. The moving edges of the image are not seen due to the scaling. While this can be extremely powerful tool to clean up the shakiness and to provide shots which look like aided with cranes, jibs, or steadycams, it can also ruin the shots completely. It really depends on the optical flow of the shot, and the type of shakiness present. In some of the cases, the stabilization plugin gives distortion into the image, or wobbliness similar to the rolling shutter effect, if the stabilization is faulty or the footage is too shaky to properly stabilize. Usually the power of the stabilization plugins lies in using them as finishing tool rather than total-solution tool. The camera operator should always work to reduce the shakiness to the absolute minimum while shooting, and use the stabilization tools for that finishing touch. And usually it is best, especially in tracking shots, to aim for smooth motion, rather than trying to smooth out all camera movement. Usually a motion to the camera is desirable, and gives a bit more life to the shot than a perfectly stabilized one.