Yes they have, but generally in different ways than the regimental or division level mass drops that you might associate with World War II.
Lt. Gen. E.M. Flanagan Jr. (retired) has a fantastic book on the history of US Airborne Forces, Airborne, that is a great place to start for a comprehensive history of the topic, at least from the US perspective.
In Korea, combat drops were used as a way of cutting off lines of retreat for DPRK forces in the period of flight after the Inchon landings and the breakout from the Pusan Perimeter. As part of the Battle of Yongju, the 187th Airborne RCT was dropped into blocking positions further north on the axis of advance of UN ground forces, with the intention of preventing North Korean forces from withdrawing. This didn't end up working out, because in the attempt to close the gap enough that the 187th RCT wouldn't be left exposed and without heavy weapons for too long, the bulk of the North Korean forces were able to withdraw north of their eventual drop zones.
The 187th was used again in a combat drop, accompanied by a small detachment from the Indian 60th Parachute Field Ambulance Batallion, during Operation Tomahawk in 1951, again with the idea of using airborne troops to insert a blocking force behind enemy lines to set up a hammer and anvil engagement.
Vietnam saw a shift towards Air Assault, with heliborne infantry largely replacing parachute drops. The ARVN utilized parachute drops, early in the war infiltrating small special operations groups into North Vietnam by way of parachute drops, and did engage in a number of combat drops. However, the ARVN didn't have the same level of institutional expertise as the US airborne forces, and these combat drops, such as at Ap Bac, didn't play a major part in the battles. The US did deploy airborne forces in a parachute drop once in Vietnam, the 173rd Airborne during Operation Junction City Alternate. Again, this was a Hammer and Anvil operation, although it was done in reverse. The concept was for the 173rd to drop in and flush out NVA and Viet Cong fighters, driving them into prepared positions manned by conventional infantry, rather than conventional ground forces driving the enemy into an unanticipated blocking position established by a parachute drop.
The Rhodesian SAS used air drops fairly extensively during the Rhodesian Bush War. A Handful of Hard Men by Hannes Wessels was a very well written and entertaining book on the topic, but I haven't read enough other sources to say if it is an entirely reliable and accurate account. Rhodesian tactics often combined heliborne infantry and paratroopers, probably most famously in Operation Dingo, where the airborne and air assaulted troops formed a perimeter around a major ZANLA camp, and engaged ZANLA troops fleeing as the camp was repeatedly attacked by helicopter gunships and bombers.
Operation Urgent Fury in Grenada saw a combat drop of elements of the 1st and 2nd Ranger Battalions, with the first wave parachuted into the Point Salinas airport in order to seize and clear the blocked runway, and follow on waves landing on the secured airport.
There are certainly other cases, and hopefully someone can come in and fill in some gaps (French use in Algeria and Vietnam?) in areas, but long story short, yes, paratroopers have been used in combat drops since World War II. Over time these uses have grown less frequent, especially with the advent of rotary winged aircraft making it much easier to quickly and precisely deploy troops than air dropping, and generally smaller in scale since their heyday of divisional level drops in World War II.
Sources:
Airborne, by E.M Flanagan Jr
A Handful of Hard Men, by Hannes Wessels