This video by OutdoorAdventures demonstrates using Glock pistols for hunting medium-sized game. They are using extended barrels, and I presume the Glocks are loaded with 10mm Auto. (Animals are being shot in the video)
I am not an advocate of hunting with pistols. I don’t believe that 99% of handgun owners can shoot well enough to be hunting with them. Anyone who starts hunting with a pistol should start by using a higher-powered pistol chambered in something like .44 Magnum, .454 Casull or .500 S&W and only move onto lighter cartridges, such as the 10mm Auto and .357 Magnum, when proficient enough to ensure a clean kill.
UPDATE: Clarified by comments on handgun hunting. For the record, I am not against it, but just like I also don’t think 99.999% of rifle owners should hunt dear with .22 LR (but I know a couple who can).
UDPATE: Steve on Handguns.
[Hat Tip: Caleb @ Gun Nuts]