The 1. Fallschirmjägerdivision (7. Fliegerdivision prior to 1943) : The 1st Airborne Division fought in Russia after the Battle of Crete. It was divided in several battle groups, fighting both in the north of Russia and today's Ukraine.

After the assault on Malta was cancelled parts of the division fought under Rommel in North Africa. After the retreat they were stationed in southern France until Operation Husky (allied attack on Sicily). They were no deployed (via parachute jump) to Sicily were they fought as what we'd today call a "Quick Reaction Force". They were among the last units on Sicily and then fought in various battles in Italy, like Monte Cassino. They saw the end on war between the Po River and the Alps.

The 2. Fallschirmjägerdivision fought in Italy as well (they liberated Mussolini in the "Unternehmen Eiche", and was later deployed in France. They got annihilated in the Battle of Brest, until a new division under the same name fought in Holland.

The 3. Fallschirmjägerdivision fought in France after the D-Day. They saw action in Falaise were most soldiers fell or were captured. They didn't fight major battles anymore and got drawn back to Cologne, were they surrenderd in the Ruhrkessel.

There were plenty of so called "Airborne Divisions" in the Wehrmacht, the only one that actually did airborne fighting was the 1. Fallschirmjägerdivision and parts of the 2nd. In the others the majority of soldiers wasn't even trained in parachuting. After Crete Hitler didn't value airborne fighting anymore, he considered the element of surprise was gone now. This and the complete lack of air superiority, especially on the western front, modeld the Airborne divisions to normal/light Infantry divisions. They held the name "Airborne" for prestigious reasons. There were some more jumps after the Battle of Crete like the Operation Stösser, but they weren't very successful due to lack of training.

If you want I could try and put together a list of German parachute jumps in WW II after Crete, but it could take a while and I doubt it would grant that much insight.