...and cutting off their fingers as a pledge of loyalty? I'm looking at you, Assassin's Creed. They're going to need those fingers in combat! Wouldn't a simple pin-prick blood oath do the trick? Sorry, just had to point that out.
shareIt was an ancient tradition in the historical order. The games/movies are just copying it trying to look clever.
Also "payment in fingers" was actually pretty common form of punishment.
As far as Assasssin creed goes, it was specifically to use the hidden blade device. you activate the device with the stump of the finger you cut. However in the second game Leonardo Da Vinci (yes that one) modifies the device so the protagonist does not need to cut fingers off anymore.