U.S. soldiers are not supposed to, but it does sometimes happen.
Kentucky rifle and Brown Bess muskets captured from the British.
Units who want to make a display of them are able to, with approval, but individual soldiers cannot do this. In Iraq, NOTHING could be brought back as a war souvenir - not firearms, not flags, nothing. Firearms, definitely not. IIRC, a soldier in the Minnesota National Guard tried bringing back two AKs. He was caught, and sentenced to ten years in federal prison.
I was there looking around yesterday, I didn't see anything. They do have ammo pouches, slings, and things like that there, but nothing airsoft related.
Some SKS rifles were brought back... most of them were manufactured in East Germany or China, as the Vietnamese made SKS rifles were and are extremely rare. They were either captured or sold/traded for favours to other soldiers in-country.
The standard infantry rifles in the RCAF are the Diemaco C7A1 and C7A2 rifles.
Lt. Pumpkin in the book Johnny Tremain Who was a British soldier. Johnny helps him desert from the army. Later, Pumpkin is captured by the enemy and executed.
Santa Anna was the military leader captured by the Texan army.
The Mexican captured the company flag.
Kentucky long rifles.
When the enemy gets a nuke
AK
Yes.