The airborne forces in World War II were very effective in my opinion. From the start of the war until the end, they secured many objectives that would have been difficult or even impossible to come by conventionally.
In 1940, the Blitzkrieg through Holland and Belgium was led by the Wehrmacht's Fallschirmjager who dropped in hours before to capture key strongholds and bridges. These operations were completely successful and allowed the German Panzers to move much quicker across what would have otherwise been an extensive delay, or halt.
In 1941, the famous Crete invasion was a complete tactical blunder. The German High Command used the troops as the invading force rather than the supporting force. This is why their losses were so high, and the tactical gains so few. The island was taken however, which proves some success even when the High Command orders the wrong troops in.
The invasion of Italy was marked by the dropping of U.S and British airborne on to the mainland. These units did become scattered but achieved objectives behind enemy lines, and prepared the path for the landing forces.
The invasion of Normandy, well known, was opened up by the airborne. Dropping behind enemy lines, the British 6th Airborne secured the left flank of the invasion forces by destroying several bridges and capturing a few more. As well as halting artillery fire that would have come from the Merville Battery.
The U.S troops, as we know, became scattered all around Normandy. But they still achieved some goals, and the confusion of the drop zones played havoc with German planning. These units also secured vital road links off the beaches, one such place was Carentan which was secured by 101st Airborne to allow V Corps tanks off the beaches and on to the grassland.
Operation Market Garden, while a failure in the end, was a good example of effective airborne troops. The 101st and 82nd managed to secure objectives in Eindhoven, Son and Nijmegan. While 1st Airborne managed to capture most of their objectives in Arnhem. The plan itself was fine, had it been done in August. The timing of the operation was wrong, not the usage of airborne.
And finally the drop on the Rhine. Which carried the offensive across the Rhine and into the German homeland. Probably not possible without the 17th and 6th Airborne divisions landing over the east bank.