I guess "close" is relative... usually, I try to keep equipment, a minimum 5 feet from aircraft and jet bridges, especially if there might be a blind spot with a covered cart or an air start and unable to see while pulling away in rig. Obviously, belt loaders and lav trucks will be closer than 5 feet, but anything else I try to keep my distance. If I am moving carts around a belt loader and there are some funny angles, then I will ask someone to spot me, so that I don't hook a cart on the end of the belt loader.
As a side note, one guy in LAS hooked a bag cart on the end of a belt loader while pulling away in a rig, thus crushing both legs of the agent who (stupidly) left his legs dangling out the bin door between the door's edge and the belt loader. 6 months later and he still hasn't returned, so let's be careful out there!