mofosaurus:
The "best" depends on what you are trying to define as the best.
Hostage rescue - SAS (Delta blew it outside Tehran)
I see a lot of references to elite units, etc. throughout history. In one message, a person mentions the failure of Delta in the Iranian desert. Yes, this mission failed, because of transport problems, beyond the control of the Delta unit and it's commander. We did learn from this tragic event, in the Special Operations community though. Many things have changed since then, particularly in the transport units both Army and Air Force. I think that this person should also consider the fact that the Delta unit has performed many successful missions and operations that he or you will never hear about and continues to do so every day. This is true of the whole Special Operations community which consists of the Delta Force, Rangers, SEALs as well as Special Army Aviation units and Air Force Special Operation units. Recently the Marine Special Operation units (Recon) have been added to the Special Operation Command.
Another such raid that Technically failed, was conducted by the US Army's Special Forces "Green Berets." This was the Son Tay POW Camp raid, conducted in North Vietnam during the war there. The POWs had been moved and as a result none were rescued, however; many "foreign" SAM missile technicians were killed during the raid. The raid was planned and executed flawlessly by a very brave bunch of volunteer Special Forces soldiers under the command of COL. "Bull" Simons. Although no POWs were rescued, ask a former Vietnam era POW what effect the raid had on their life in captivity.
I will not even get in to Special Forces led SOG operations conducted in Laos, Cambodia, North & South Vietnam. Some of these "operations" are still classified.
I would also mention some of the heroes of the "Cold War" that you might not have heard about, as much of it is still classified. Top in this group, are the US Navy's Submarine force and its assigned SEAL or Navy divers. (How about tapping a USSR underwater communication cable, in their waters.) The many reconnaissance flights by the Air Force, Navy and CIA during the span of the cold war and continuing even today in many parts of the world, especially around Korea, China. Many have given their lives in this endeavor, especially in the cold war.
As for American elite units and/or brave acts in WW II there are so many that no doubt forget to mention some, however; I will try:
Defenders of Wake Island (Marines)
Defenders of Battan, PI (All Services)
Battan Death March PI (All services)
Underwater Demolition Teams (US Navy)
Torpedo Sqd 8 (One surviver- US Navy)
US Army's Special Service Force Division (US Army/Canadian)
US Army Ranger Battalions (especially the 2nd Bn's climbing of the Cliff at Pont De Hoch)
US Army's Alamo Scouts (Pacific theater)
US Army's Merrial's Marauders (Burma)
US Army's 101st Airborne (Normandy/Battle of Bastone)
US Army's 82nd Airborne (Normandy/Many other Battles)
US Army's 11th Airborne (Pacific, Especially the jump on the "Rock"
US Marine Parachute Unit (Pacific)
US Marine Raiders Unit (Pacific)
US Navy Submarine Service (Pacific)
One foreign hostage rescue unit not mentioned also has had some great operations is Germany's GS G9.