Help to find good anti-shake camera?

I want to buy camera, but don't know which is better for anti-shake. I want to take photos of moving subjects ( for example, jumping person, swimming, and etc.). I want to buy one of these models:

Nikon d90
Nikon d 3000
Nikon d 3100
Nikon d 5100
Nikon d 7000

Canon 1100d
Canon 650d
Canon 600 d
Canon 550d
Canon 500d
Canon 60d
Canon 50 d

Actually i don't care Canon or Nikon (I like Canon, but think that Nikon is better), i just need that when i take moving photographs ( for example, jumping, swimming, and etc.) it would be good photo. Which of these models would you advice? And may be you can advice any model out of list? (preferring Canon or Nikon) I know in some lenses there's anti-shake system, but i want to buy camera that has anti-shake system in itself, not in lens. I think something about $ 600 -1300

If you hold the camera correctly, there's really no reason to use the VR or IS feature on the lenses you use

Any of those cameras can use image stabilization lenses, but framkly, if you are shooting at 1/500th second or faster (the shutter speed you need if you wish to stop or freeze the action) you will have that feature shut off on the lens any way.

Here is a sample of a shot, taken with a 300 mm f/2.8 lens with the VR shut off.

Of the listed cameras, the Nikon D3200 (replaced the D3100) and Canon T3i/600D will do the job. All you have to do is buy the lenses you need to shoot action, sports and some wild life.

The lenses will cost more than the actual camera.

The above two cameras cost under $700 with a standard 18-55 mm lens. The long lenses you need will cost much more. The 300 mm f/2.8 lens used for the night football shot costs nearly $6, 000

I love the D7000 for wildlife where I have to shoot from a moving vehicle without any support.

Rumour has it, a d600 is on its way. That will:
- be a full frame version of the d7000 - it will be new and not out dated for a while yet costly, I would guess outside the budget you have indicated.
- it could also drop the price of the d7000

We didn't have anti-shake during the film era and we still managed to get stunning shots. It's how you set-up the camera. Any will do. Consider them the same.

Canon and Nikon install their anti-shake system in the lens. Some lenses have it, some don't. They argue that the system is better if it's in the lens but I see it as a ploy to offer multi-level pricing schemes. Sony and Pentax have their anti-shake systems in the body so all lenses benefit from it, even those old antique fully manual film lenses of yore.