There are still weapons and aircraft, such as the B-52 and C-130, that have served since before the Vietnam war and are still in service. Were there any weapons or aircraft that served in both World War II and Vietnam?

The M1 carbine was adopted during ww2 for infantry use and saw extensive service during both the Korean and Vietnam wars. It was still a standard infantry weapon during the early years of Vietnam, but was phased out gradually, so that by the fall of Saigon they were mostly replaced by M-16's. They remained popular throught with units though due to their light weight, and were used extensively by special forces and many were given to the South Vietnamese Army.

The C-47 transport aircraft saw use in ww2 as a cargo carrier and for airborne operations. By Vietnam most were out of the inventory, but there were some left laying around, and the U.S. converted them into the AC-47 "Spooky" gunship by essentially sticking miniguns and machine guns out of the side and turning gradually. This was the precursor to the wide variety of AC-130 gunships that are still in use (and being updated) to this day in the same role. It should be noted that the AC-47 program itself had mixed results, because while they did wreak havoc on troop and equipment convoys, i'm sure you can imagine the problems that come with flying an aircraft in a low level circle, slowly, around an enemy force armed with anti-aircraft weapons.

Those are two examples, I know that a fair number of U.S. tanks that were developed near the end of WW2 were used in Vietnam but I don't know enough about that to really say much. Someone else will, i'm sure.