I remember the British SAS guys taking shots at our Green Berets by saying something along the lines of, "American special forces can't operate without a Burger King and a street lamp nearby" which I thought was telling of their own capabilities.
All time best story I ever remember hearing though of a SpecOps unit was regarding the Russian Spetznaz (sp?). Those guys get selected by being blindfolded in a room for a period of time, then viciously assaulted by an unknown, unseen assailant, then as a final option, given a choice of being stabbed with a knife in the side or having their arm wrenched behind their back until it's broken. Choosing either and coming through it with the least amount of "display of pain" warrants selection for training after healing up. Failue to agree to either or acting too hurt rules you out.
I also remember in the same recount of a Spetznaz operation where in a hospital, unarmed, a single Spetznaz soldier killed 20 armed guards/soldiers with little more than a scalpel and the weapons acquired from the fallen. In another story, the Spetznaz, after the Iranians hijacked a Russian airliner and killed several passengers, they were dispatched to the hometown of the hijackers where they killed their entire families, to include pets, poisoned the local water supply and burned their houses to the ground, then played the video tapes of it all to the captured hijackers before killing them for their crimes. That's some hardcore shizzle.
US Military I'd have to guess that Delta Force is the premier "not secret" force, although I've heard rumor of a more elite, unknown group of soldiers that belong jointly to the CIA and the Pentagon that conduct covert operations you'll never hear of. BTW, Delta Force was once led by the new Army Chief of Staff, a guy I would not want to meet in a dark alley alone or with 10 other friends of my own even. I have a fellow MP friend who's a former Special Forces soldier (yes, for real, I've seen his offical records) and he said that in the final portion of their training, an exercise commonly referred to now as Robin Sage, they have to parachute down to their LZ, then march with all their gear better than 25 miles back to base camp for graduation. He said that Gen. Schoomaker, the new Army CoS met them half way and actually helped carry some of their gear as well as any soldier who was having a hard time, this, in addition to their own gear they brought out with them. He said the guy was close to his 40's then, helping to carry the gear of these 19-25 year old guys nearing completion of their SpecOps training.