Do magnetics connectors exist?
Apple has a patent on a technology called MagSafe that uses spring loaded pins and a magnetic shell. This handles the limited mating cycles problem to an extent. Until the springs in the pins wear out. And since it has little to no friction holding it in place (it uses the magnetic force instead) it can disconnect easily when someone trips on the cord which is seen as a safety measure. However this does not address the problems of impedance and isolation.

Inductive Charging works like an air-core transformer (though there is usually plastic in between the coils as well).This is what Paul mac was referring to when he referenced cordless toothbrushes and Barry was referring to when he mentioned electric car chargers. There is also a group known as the Wireless Power Consortium that is pushing a a standard called "qi".

I have a "qi" type back for my cell phone that allows it to be charged by placing it on a special plate. I also have a Sonicare toothbrush that uses inductive charging. Both systems work great. They give essentially unlimited mating cycles as well as provide great isolation. My toothbrush regularly gets covered in water and toothpaste without any detrimental effects.

Both these systems are used for carrying DC charging current. Both systems look as if they could be used to carry an AC signal or a digital signal as well. Though I'm not sure how high a frequency/speed you could attain using such a system. And, at the moment, I do not know of any standards/connectors that are doing so.