Just to be clear, the computers onboard the spacecraft are programmed in assembly language--3 types of computers on each spacecraft, so 3 assembly languages.

The original ground system was mostly written in Fortran. Mission control (i.e., the thing you see on TV!) ran on IBM 360 mainframes. Offline analysis/design/development activities (e.g., developing observation sequences for planetary encounters) ran on Univac 1108 mainframes. Circa 1990, after Voyager 2's flyby of Neptune, the project began moving off the mainframes onto Unix workstations and the original Fortran software was largely replaced by new software written in C and other languages.