There may be more I don't know about but I put what info is known below. Some of it comes from this article:
http://www.gamespot.com/features/the...ng-us-6403460/
Standard Arrows: unlimited (can be charged for greater damage, GA does not have to stay stationary to charge)
Fire Arrows: 3 (can cause burning damage over time, even when opponent blocked the arrow)
Stun Arrows: 2 (causes short stun)
Ice Arrows: 1 (causes a longer stun)
Exploding Arrows: not selectable like the fire/stun/ice arrows but rather it is used automatically in certain special moves (I suspect that the EX version of the normal arrows makes them explosive as well)
Bolo-Grapple Arrow: seen only in GA's "Super" move to pull opponent back to the ground
Zip-line Arrow: not available in combat, used in GA's entrance animation
Green Fireworks Arrow: not available in combat, used in GA's victory animation