Do F-4 Phantom II pilots actually fold the wings?
As several of the comments have mentioned, the F-4 have the option of folding the outermost section of their wings, as shown in the picture below. 

The main purpose of this was simply to save precious space on aircraft carriers, it had no use when flying. There have been some incidents where wings have either started to fold during flight or where the pilot forgot to unfold before takeoff, but it was not designed for this. Many other naval aircraft have the option of folding their wings in a similar manner, such as the F/A-18. 

The F-14 Tomcat uses a completely different mechanism to adjust the wing sweep while flying, and although it had a special "parking setting" for the sweep, it was used to adjust the wing sweep according to the speed of the aircraft. 

The A-7 Corsair II and the F-8 Crusader also had wing folding, but in addition they could also adjust the attitude of the wing while flying, primarily to improve visibility for the pilot when landing as seen below.