What was the lowest ground speed landing? Planes fly if their speed relative to the air is high enough to produce lift. If there is no wind, the plane's air speed will be the same as its ground speed. If flying against wind, its ground speed will decrease.

That said, what was the lowest ground speed during landing ever recorded?

I think there should be some rules against landing with the wind from behind, as it would make the plane go too fast, but what about opposite? Has any plane landed with zero, or close to zero ground speed? How about 'negative' speed, pushing the plane backwards relative to the ground?

I found some information about the highest ground speed while in flight, but I'm interested in the exact opposite.

Highest points for answers with passenger airplanes (737 etc), helicopters are considered cheating.
Considering groundspeed as a vector, 0.  

You can land vertically with strong headwind: Could a plane land vertically in a strong headwind?

As the answers to the question, previously linked in Flexo's comment -  Is it possible to fly backward if you have really strong headwind? - detail, the answer is "yes". It's even possible to have one's groundspeed vector directed tailwise. 

The Antonov An-2, can be flown at as little as 25 knots of airspeed, and safely landed below that speed. When turned into decent headwind, it can be kept in hover relative to the ground. I haven't found a video of a hover landing, but it's been reported to be done. With a 12-passenger capacity, it's no 737, but it can count as a passenger airplane, and it's designed to do this.

Vertical landings of smaller planes have been filmed: 
                
             (thanks bukwyrm).

P.S. Vector representation is most appropriate for groundspeed, as it's not normally directed along the aircraft's longitudinal axis due to side winds. So landing "backwards" can be considered positive groundspeed once again.