If hunting with a semiauto rifle is legal where and for what you intend to hunt, as has already been suggested, there can be a variety of calibers available.

Generally though, the AR-15 is a .223 (not legal/sufficient in some states for big game). HOWEVER... Numerous options can be had that "fit" an AR-15 lower reciever that might be better hunting rounds: 6.8 SPC, and a bunch of .45-.50 caliber jobs such as the Bushmaster or the Beowulf.

On the other hand, an AR-10 is capable of handling longer cartridges through its magazine well and action, such as .243, .308, the WSSMs, and even a WSM (I think), etc. A bit more expensive, but if you want to be able to hunt big game, the AR-10 platform is probably going to be your better bet.

I hunt turkeys, coyotes, and prairie dogswith my AR (and a five-round magazine to be compliant with local laws). My most often-used load is a 60 gr Hornady SP backed by Varget or BL(C)-2. For varmints exclusively, I've been using 50 gr V-Maxes and Varget.