It is to do with accidents and disease - im not sure of the name but just recently someone asked this question or one simular and the name was given there. The question was originally asking if pigeons are vermin and we pretty much decided that they were dirty flying rats ; )
One of the reasons is that when its cold weather and pigeons sit on Telegraph wires their feet freeze onto the wires. When they come to fly away as their joints are so frail, their feet stay attached to the wire and they fly off without their legs.
Also, apparently it is 28% of pigeons which only have one leg (in London)
Also they don't keep their nests clean - as a result the chicks get muck stuck around their toes which dries rock solid. Then more muck gets stuck on etc until they have solid balls around their toes. As the toes grow they get squashed until the blood supply is cut off all thogether and the toe dies and falls off - we used to keep pigeons and were forever having to clean out the nests and break the dirt balls off to prevent this happening. Yuk! They really are dirty birds!