The Germans were actually pioneers in the realm of airborne infantry, and while other Axis powers did have some airborne troops they never achieved the success the Fallschirmjaeger did. In the early parts of the war they dropped in and seized strategic locations in Poland, Norway, Belgium and the Netherlands. The most succesful attack being that of Storm Group Granite against the Belgian fortress of Eben Emael when 85 Fallschirmjaeger seized the fortress from 1200 Belgian defenders.

All of this culminated with Operation Mercury, the German airborne assault on Crete. Unfortunately for the Fallschirmjaeger the Commomwealth and Greek forces were far more numerous than they were expecting, and they were forewarned due to Enigma intercepts. This, combined with the fact that the German parachute system (single riser in the middle of the back) didn't really allow dropping with a main weapon, meant that they were landing and having to immediately fight against a prepared enemy with nothing more than pistols, knives and grenades.

Through perseverance and offensive spirit the German forces captured the airfield at Maleme and were able to airlift in more men and supplies to salvage the operation. Casualties were horrendous though, and Hitler forbade mass airborne assaults in the future. German airborne troops operated on all fronts as elite light infantry throughout the rest of the war and executed the occasional small scale operation, but were never a strategic weapon again.