My gates for pastures that I mostly drive my tractor into, and might on a rare day, drive my pickup into are 12 feet. This is what I consider the bare minimum.
I put in 16 foot ones on some land I had that worked our real good. That might sound like overkill, but the price difference is minimal with ALLOT more room for comeing and going.
Lets say you got things hanging off a vehicle like tow mirrors or something. We can use 9 feet as a safe width for vehicle traffic.
A 12 foot gate will give you 18 inches on either side to drive through before you hit something. To me, that's too tight for a primary entrance without offering any advantage to such a small opening.
My entrance is 24 feet wide with two 12 foot gates. I plan on having RV's, trailers and allot of traffic coming through mine. I've found the more room you have to manuver, or even line up for a straight shot, the less problems you'll have.
Eddie