A typical backhoe will fit through an 8' gate, at least those I'm familiar with. My tractor and bobcat are both 6' wide as is my zero turn mower with the 60" deck so 8' is a reasonable minimum. However, that is pretty tight and requires care. The nine gates I installed here on the farm are between 12' and 16', with 14' a comfortable size for large horse and equipment trailers. A wider gate not only gives room going straight through but also for moving through at an angle and especially when backing a trailer. But I'm using these gates all the time. For occasional or rare access for vehicle, equipment, or small trailer an 8' gate should work. If you want to provide for trucks or larger trailers (my big trailers are 8' wide) a 10' gate would be tight but would work.
JKJ