Currently, only the four MFT-FT adapters by Panasonic and Olympus offer nearly full compatibility to original FourThirds lenses. I say nearly, because some FourThirds lenses are not compatible with all MFT cameras. E,.g. some old FT lenses are not compatible with the contrast AF. And SWD lenses generally perform not so well on MFT. And the aperture ring on the Panasonic/Leica FT lenses works only on Panasonic FT/MFT bodies.
There was a compatibility list on the Panasonic website, but I was unable to find it now.
The current adapters to all other mounts are non-electronic and allow you only to focus manually.
Those FourThirds to MircoFourThirds adapters allow for autofocus, however check the compatibility for every camera/lens combination:
MMF-3 (weather sealed)