My wife asked me to ask this:
We live in a normal, suburban neighborhood, and have begun to notice partially eaten ears of corn near our home. There are two on the outside sill of my upstairs bathroom window, and one on the ground outside my back door. Still two more lie outside my front door.
Who is leaving them there, and what do they want?
What kind of corn? Is it seed corn, indian corn, or roasting corn (corn on the cob-type)?
If it’s seed corn, someone may have left it out for squirrels to eat.
If it’s indian corn, it may have originally been intended as someone’s decoration, which got carried away and wound up on your house.
The question of exactly how it GOT there is still a puzzle, though. We used to leave corn out for the squirrels in the winter, and they could sometimes manage to drag it off, but usually they didn’t get very far with it before they dropped it on the ground. My best guess is that some teenagers threw it up there as a prank.
One other possibility: if you live in an area where there are raccoons, they might be responsible at least for the ones outside your door. They’re large enough to carry an ear of corn away.
Could be tree rats (a/k/a squirrels); they ate the ornamental corn hanging outside of my house a few years back. If this is so, the tree rats are probably looking for a quiet place to eat where the myriads of predators that they have (wild and domestic canids, snakes, automobiles) won’t interrupt them.
Of course, if you live in the middle of the desert, this explanation is probably wrong 
It is often said that “anything is possible”. In fact, very few things are possible, and most of them have already happened.
My folks used to put corn cobs out for squirrels until they found out the squirrels were driving their neighbors crazy leaving corn cobs all over their yards.
Squirrels tend to eat a little when they pick something up and then hide or bury the rest. And they are a lot better at hiding stuff than they are at finding it again.
“pluto … a seriously demented but oddly addictive presence here.” – TVeblen
Another possibility is stray dogs. Although largely carnivorous, I’ve seen dogs pick up ears of corn and carry them around. (I used to live on a farm.) Why they do it? Who knows. Maybe it’s just because they can.