All superzoom (prosumer) cameras have some form of image stabilization (IS). Most late model cameras have "mechanical" image stabilization - (1) sensor shift (eg. "CCD shift", though more point & shoot cameras use CMOS now) (2) optical.
The camera also raises the shutter speed (eg. by opening up the aperture and/or increasing the ISO setting) to help reducing camera shake, if you are using the "Sport" scene mode.
The image stabilization system of these cameras is usually effective to gain at least 1 to 2 "steps" of shutter speed - if you go by the traditional rule of "1/200 sec speed for a 200mm lens" (NOTE: this is more applicable to old SLR cameras with large clunky telephoto lens. Many people can manage at least 1 "step" lower shutter speed in smaller point & shoot cameras without IS), image stabilization allows you to use 1/100 or 1/60 sec or even lower shutter speeds.
A camera with a "fast" lens (ie. large aperture / small "f" number) potentially allows a faster shutter speed and reduce camera shake. Unfortunately, zoom lens have variable "f" numbers (ie. the largest aperture decreases as the zoom increases) - most superzooms which are 400mm+ at the telephoto end have f/5.6 or higher, which is of little help. If telephoto zoom is important to you, DON'T just look at the smaller f-number (eg. f/2.0 of the Canon S90) - manufacturers always advertize the "best" feature which is not always the full picture!
The best way to assess the ability of the image stabilization system of various cameras is to read up on camera reviews. However, I think they are pretty much the same in effectiveness.
Therefore, I would worry more about other capabilities of the camera such as optical quality, low light capability, size/ weight, user friendliness etc. IMO, Canon and Panasonic Lumix have the best optical quality. Fuji used to have an edge on the low light capability, but other manufacturers are quickly catching up (or Fuji is slipping). I agree with Cinema Face that all current prosumer cameras are no match to DSLR in terms of low light capability (and optical quality), but this is a tradeoff for an all-in-one camera.