Swords actually have been used in recent combat ops by the US military..... well sort of.
Back in the fall of '03, I was about midway through my wonderful 358 days of fun in the sun OIF1. I was a M1A1 tank commander and had recently "found" this huge arabian looking sword and had it stashed right next to the TC hatch on top of the tank.
Anyways, my tank platoon had quick reaction force duty one day and we got called out for a traffic accident outside the wire involving a civilian car and a Bradley right next to an outdoor market area. Normally you would just get the heck out of the area when involved in an accident as it had been a tactic used to get us to stop so we could be attacked. The Bradley had messed up the track so they could not leave so they called for backup. By the time we got there, a crowd of civilians (crowds=bad) had gathered nearby and would not disperse or leave no matter how hard we tried to chase them off or how loud we yelled "get the **** out of here!" in english (I'm sure they got the message though). So I improvise and jump off the tank with that huge arabian sword, waving it around and generally looking very pissed-off. Before my feet hit the ground, that crowd was gone. I have never seen people run so fast!!! That sword stayed on the tank for the rest of the tour and handed off to the unit that replaced us.
So, yes swords are still being used in modern armies and have been proven to be very effective in modern conflicts