How limiting is lack of image stabilization in Pany bodies?

Lot of good answers here.

I'll just add that the advantage of IBIS is not restricted to longer focal lengths. I routinely take pictures with the 12mm and 14mm (neither of which are stabilized) that I wouldn't be able to get without it. 
With IBIS I can safely take pictures down to 1/3 second with the 12mm, and I do, in order to deliberately capture motion blur against an in-focus background.

That being said, most situations--certainly most situations outdoors--don't require IBIS and some claim that leaving it on can induce some blur. I've had and enjoyed several Panasonic bodies and really only missed IBIS a small fraction of the time.

Also don't forget that many great Panny lenses have OIS, so IBIS really isn't needed at all. If you shoot mostly with the kit lens or longer, for example, you probably won't care because all the kits and telephotos have OIS.