I've been building and using gates on my farm for the last 10 years, and when I first started I believed (honestly) that an 8 foot gate was a good size.
After bashing multiple 8 foot gates, I went to a 12 foot gate as my standard size, and after bashing a bunch of those, I finally settled on a 16' minimum gate size for vehicle gates, and most stock gates.
It seems like overkill to have a 16' gate, but I can tell you from personal experience that I've NEVER said to myself "gosh, this gate is just too big!", but I can't tell you how many times I've had gates magically shrink when I was trying to get through them. Most of the time you're not straight-on a gate, and the loss of a couple of feet makes a big difference. Yes, you can get a 6' wide tractor through an 8' gate. No, you won't enjoy it.
The picture above shows two fence designs for a gate off a road. I do these sorts of gates for field access anymore because it's safer and easier - safer in that I size the opening so that I can pull my vehicle/tractor/trailer or whatever off the road completely before I get out to open or close the gate. Now this sort of gate is easiest (for me, anyway) when it's arrange as it is on the right hand side. If you make the gate area square with the outside fence you end up with a very sharp angle at the point of the fence, and with less usable area for the gate. if you put in a big gate, you want to be able to use every inch of it. The design on the right has the area of the fence where the gate is mounted at right angles to the pull-out for the gate. That means when I pull out and align myself along that fence I'm good and have maximum gate area.
This final picture is a combination of these two gate techniques. the gate itself is mounted where the little square is. If you do it this way your gate can both block the road by swinging out - which is handy for things like herding livestock, and can open as wide as it can be. The blue circle represents the swing of the gate.
I'm a bit divided on whether or not having a short extension is worth it on the free-end of the gate.