I live in the sticks, too, so I can sympathize! My favorite story is the time my family came back from vacation to find our back yard filled with cows...they were everywhere...even on the brand-new deck my dad had built around the pool!
Let me tell you, it took a good amount of scrubbing to get the cow patties off the deck! Turns out, the cows belong to our neighbor, who refused to take any responsibility when my dad told him that the cows had messed up our deck AND our chain-link fence (they had crawled under it...don't ask me how). And do you know what the neighbor said? "You should have known your fence wouldn't keep out my cows." Meanie.
*edited to add* Then one time, my parents came home to find a little pygmy billy goat running around the yard! It scared my sister to death because she thought it was a dog at first, but then it went flying past her and she got a good look at it. It was a really cute little thing and it had a collar on, but we couldn't figure out who it belonged to. We had a heck of a time catching it...don't tell my parents, but I accidentally let it in the house trying to catch it and it kept butting at the sliding glass door...I don't know how I would have explained THAT one if the door had broken BUT I finally got it back outside and made sure there were no little hoof-prints on the carpet.