You can still apply the 1/(eq. ff mm) rule to 4/3, 1", 2/3", 1/2.3" or whatever sensor and take the image stabilisation (IS) into account.
First, let's postulate that on any camera and any sensor format the 1/(eq. ff mm) shutter speed is the recommended minimum shutter speed at which an average shooter will on average get about 50% shots of acceptable sharpness WITHOUT IMAGE STABILISATION ON. If you are shooting at
equivalent focal length of 600 mm without a tripod and any IS using either a super zoom P&S camera with a 1/2.3" sensor or a full frame DSLR with 4 kilos of glass attached to it (you'd be mad to go out without a tripod but bear with me), the safe shutter speed is about 1/600 s.
Now the image stabilisation or IS. Most manufactures are currently selling their top range lenses with 5-stop IS. This means that with IS ON, in theory, one can safely reduce the 1/(eq. ff mm) shutter speed by a factor of 32 = 2 power of 5. In the example above, shooting with 5-stop IS at 1/20 s should give the same percentage of sharp images as shooting at 1/600 s without IS. Even the cheapest cameras have IS of about 2-3 stops and the shutter speed can be reduced from 1/(eq. ff mm) by a factor of 4-8. Have to know your gear!
This is an example of hand-held shot I took with a Fuji X-S1 bridge camera at 624 mm ff eq, F/5.6, 1/125 s, ISO400.

I know that the IS is doing a good job up to about 2.5 stops (that's a factor of about 6) on this camera, so the slowest shutter speed I would go for at this focal length is 1/100 s (about 6 times slower than 1/624 s). Not the best shooting conditions as it was quite dark with the sun already half way below the horizon behind the heron. About 20-25 meters to the bird standing in the middle of the lake and no tree to lean on, just mud everywhere. Had it not been for IS, this shot would have been very blurry.