Point of semantics, you will never combat camera shake with a high shutter speed; you will minimize 'motion blur' that may be caused by camera shake....
You will defeat camera shake by better camera support; how you hold it, using viewfinder rather than preview screen; correct camera holding, bracing elbows, modulating breathing; or supporting with a tripod, monopod, beanbag or other fixed support.
But then there is the question of subject, angle and intent.. If you are taking a photo of a stained glass window in a church? Its probably been around a few years, it's not likely to rush off in a hurry! You don't necessarily need a particularly high shutter speed to avoid potential motion blur, just good camera support. If you are taking a photo of a marathon runner, you probably need a fairly high shutter speed to capture them before they run out of the shot; but how high a shutter speed depends on the framing and angle; If they are running directly towards you, and its a longer shot, the subject maybe less than 2/3 the height of the frame, their position and size in the frame wont change very much as they move; on the other hand if they are running past you, side on, filling the frame, then there will likely be an awful lot more discernible 'change' in the scene in any given shutter interval.
AND you may want to exploit that to actually get some motion blur to convey the dynamic of the situation; For example, using a fast enough shutter speed to freeze the body of a humming bird hovering over a flower, but one slow enough its wings still blur to show that movement. Or you may want to 'pan' with your marathon runner so that the runner is captured reasonably sharp, with a little blur around pumping legs and arms showing the motion and effort, whilst the background is more significantly blurred by motion to lift the subject into prominence from the setting. Panning, deliberately moving the camera during exposure, then makes the question of support more intricate, as you cant simply rigidly support it, and have to carefully control motions.
SO, the 'as fast as your lens length' guide of old. And do you apply the crop factor?
Well, it is only a guideline; the appropriate shutter speed should be selected from above primary considerations of subject, situation & intent, and 'unwanted' motion blur from camera shake, tackled as first course by appropriate camera holding...
The rule is a legacy of 35mm film era, in so far as that promoted the use of high tele-photo lenses so much, which was where the effective frame magnification they offered was likely to show more pronounced unwanted motion blur from hand holding; and it was a fairly reasonable 'guide', within certain limits.... for example, I have an old Russian Zenit,which has a fastest shutter speed of just 1/500th. My much more modern and sophisticated Olympus OM4 only has 1/2oooth as its fastest shutter, and many other's were rarely any faster. Popular 'big tele' with Birders in that era were Centon 'Mirror' lenses in either 5oomm or 1ooomm guises, with a fixed, f4 or f5.6 aperture; Add a limited choice of film speeds, probably no more than ISO400, fixed for the roll, you'd then have the small problems that shutter speed was the only control you had left to balance your exposure, and even before you start, you have a lens begging a shutter speed higher than your camera provided!!!!
Going the other way, of course, you might think you would be 'safe' using a 35mm wide angle lens, and any shutter over 1/3oth would 'do'.... so how did so many people manage to get blurry shots with 35mm Instamatics with such lenses and slowest shutter speeds? Probably because they were close to their subject, and filling the frame with them, 'zooming with their feet' got the same relative frame to subject ratio and the same degree of motion blur across that frame in any given time interval. So it was never a particularly hard and fast rule. AND the 'crop factor', then not so often acknowledged as such between the different formats of 110 cartridge, 35mm cassette and 120roll film, still existed and was even larger, and not deemed so 'significant' in the hand holding issue, compared to the subject, support and framing.
So, as a guideline, on a modern Crop-sensor DSLR... it's still a reasonable one, and with a 1.5ish Crop-Factor effectively magnifying the subject to frame proportions that much more, and equally any motion blur during shutter interval, adding the crop factor equivalence to the suggested shutter speed, probably worth factoring in...
Whether VR systems are any compensation is another can of worms... and I have to say, in my experience, 'probably not' or at least 'not a lot'! when my daughter started her GCSE photography and my O/H got a DSLR so not to be left out, we had a shutter-speed 'limbo' to see how low we could each go with and without VR, with a kit lens; on a static subject shot at 35mm, (50mm FF-Equiv), my O/H who doesn't have the steadiest hand, was struggling at anything much under 1/50th, even with a coffee mug only filling 1/3 the frame. Same shot at same shutter closer up, filling 3/4 the frame, it was discernibly blurry; Daughter was down to around 1/15th and managing to keep them pretty sharp even with close up mug filling the frame; With big hands and years of practice, I managed to hand hold down to about 1/1oth or 1/5th without significant blur, but I couldn't get any lower with the VR switched 'on'. Helped shakey O/H hand hold a stop slower. Similar experiment with the 300VR, didn't show any greater benefit at longer lens lengths; where it's still more a matter of subject to frame size than actual lens length; and that the suggested advantages of VR systems, are probably slightly over inflated in the ad claims and reviews, and the idea they can let you hand hold two or three stops slower, probably only hold true in a few situations; good technique and hand holding still seem to be much more effective, IMO!
For What It's Worth; in my experience of very long lenses; hand holding and camera shake is a 'niggle'; first 'problem' is with such a small field of view actually framing with one! Then, even at relatively conservative apertures, the Depth of Focus, particularly for smaller, closer subjects can become incredibly shallow and hence critical, so 'blur' can be a compound effect of subject motion blur, camera shake and simply out of focus, and so a smaller aperture to increase DoF may actually ,make as much difference as upping the shutter.
But short answer is there isn't one, but shutter speed shouldn't be directly linked to the lens length or equiv lens length, but the framing of your subject you get from it, and then set on the situation and intent of your shot.