Besides the obvious (burning them or using them to insulate), you can use newspaper to create a makeshift weapon. There is actually a name for this improvised weapon, the Millwall Brick. You can use this weapon for hunting, defense against predators, etc.
It is constructed from one or more newspaper sheets rolled and folded to create a handle (a haft) and a rounded head at the fold. The Millwall brick becomes harder as more newspaper sheets are stacked.
The newspaper sheets can first be soaked with a liquid to add weight. The blunt end can be wrapped with a shoelace or leather. The ends can be taped together and a string attached to the handle, enabling the user to swing the brick. A pencil, pen, large nail, pointed stick, etc. can be driven from the first interior side near the middle perpendicularly through the first end so that that head of the nail rests against the first interior side. The nail may be secured in place by bringing the ends towards and adjacent to each other, effectively forming a crude nail bat.