200 82nd paratroopers and Rangers jumped in Afghanistan in 2001, and 1000 paratroopers from the 173rd Airborne Brigade jumped into northern Iraq during the invasion in 03. A total of 6000 paratroopers jumped on panama in 89, and another smaller jump of 500 in grenada in 83.
Just a list of some recent combat jumps. There was also another jump in Afghanistan on october 22nd of 2001.
There were also special forces jumps in desert storm. So during every major military operation since world war 2, there has been a combat jump by some unit of the U.S. Army.
That being said, I completely disagree with previous statements that Airborne is a dead concept. I've been to both Air Assault and Airbone school, and I loved them both, but they are two different missions, hence why we keep two seperate divisions.
Airborne divisions are used to put an independent sizable force (up do a division) behind enemy lines by surprise. With today's aircraft, these units can be delivered anywhere in the world on short notice. These units are dropped behind enemy lines to cause havoc, to confuse the enemy, and to split the enemies forces (as was done in Iraq in 03) from one front to two fronts. However, once on the ground, they are light infantry and until reinforcements arrive, can only move as far as they can march.
Helicopters have a combat range of 300 to 400 miles. They are low flying and it takes a huge number to move a division sized force. The helicopters and soldiers have to be marshalled in theatre, due to the limited range of the choppers, and have to be properly prepared. Once ready for action, the unit is rapidly deployable to exact locations and have the ability to carry heavier equipment such as artillery and vehicles. Also, once deployed to a forward position, they can reboard and jump to yet another position quickly, something paratroopers cannot do.
Obviously both types of attack have their pros and cons. That being said, no one is better than the other. That is why we have both the 82nd airborne, and 101st airborne (air assault), instead of two airborne divisions or two air assault divisions (even though we have many smaller airborne and air assault capable units, im just talking about division size).