If you don't store your canoe correctly over the winter and otherwise when not in use, you could end up damaging it. Wood canoes are prone to rot, plastic and kevlar canoes can be degraded by the sun, and aluminium canoes generally don't care what you do to them because they are tanks.
Pretty much just keep your canoe out of the sun and away from moisture. Store it upside-down raised above the ground.
If your canoe is made of different materials (metal rivets, etc.), keep it from experiencing wide swings in temperature. The different materials can expand at different rates, causing cracking and popped rivets. Indoors is best.
If you have a very light canoe, you might have an easy time storing it on some hooks up high indoors.
You can buy a UV protection spray for your boat if you need to leave it outdoors. It's sunscreen!
If you cover it with a tarp, keep the tarp off the boat. You don't want water collecting between the boat and the tarp and wrecking the surface.