At what shutter speed is a tripod needed for a D800

I've seen a couple references stating a tripod is required equipment when shooting with a D800.  I'm told it is because of the high pixel count, the camera notices shakes much easier.

I usually can go handheld down to 1/30 of a second on my D70.  What is the miniumum shutter speed would you recommend, (generally) to avoid significant shake with a D800.  I do suppose it depends on the quality of the lens too.

bc