Here's the way I like to use GGs.
First off, the only good neighbor is a dead one, especially in MP.
I'm usually playing as Zulu or Mongols, which means I'm going for a fast strangle at my closest or most dangerous neighbor. IF I manage to kill my first conquest pre-catapult, chances are I've kept the cities I wanted, have gotten my first GG, and am eying another civ to kill.
In this case, I use the GG as an instructor in my 2nd most productive city, explicitly, in the case of mongols, the city WITHOUT a ger, which is busy pumping melee. At this point I can pump exp 6/5 melee units, pre-theo, pre-fued. I use these to pump double woodsman axes (and sometimes spear and sword), or double hill archers (and later crossbow and longbow). In my 2nd declaration of war, then, not only am I beelining it to my new opponent's metal with impi or keshik (or whatever), I'm supporting it with 2-move axes, presuming I'm still early enough to get there before the enemy has chopped all their forests (most people leave some for post-math chops).
This also works well if someone mounts an early attack and good for countering furing the first war after I've killed off their early chariots/archers/whatever.
Imagine combining impi or keshik with jags or gallic warriors which are axes, and you get the idea... extreme choke until the catas mop up their cities
