There's no reason why Minecraft can't have its own papercraft models too.
Papercraft and videogames are like two peas in a pod, and often papercraft artists put together amazingly detailed creations. Heck, one guy even made a papercraft clone of himself. Just because Minecraft takes place in a world where everything is made of simple cubes doesn't mean it can't jump in on the papercraft fun too.
Sure, most Minecraft objects don't involve an incredible amount of folds, but they're still cool. One papercraft creator has proven the Minecraft joy that can be put in your home thanks to papercraft that isn't terribly stressful to assemble.
One source for making your own real world Minecraft cubes is available on the game's forums, featuring blueprints to make a game character, pig, chest, block of TNT, and many more objects. Who knows, maybe people will build their own flammable and absurd Minecraft objects in real life now using Minecraft papercraft. The possibilities there are just blowing my mind.