This story is an old Romanian folk tale and the version repeated here was originally found on the internet here.
You can buy a book containing this tale from Amazon.co.uk.
We all know cats love to sit on the doorstep, but do you know why? This story goes back to the days of Noah and the Ark (You do remember that story don't you - how God commanded Noah to build an Ark and to take aboard two of every animal and bird to repopulate the world after it was destroyed by a great flood.) Noah had worked for a hundred years to build that great boat out of gopherwood and he had put in as many years trying to warning mankind of the impending doom that would be coming because of their sin. They only laughed at Mr. Noah, building that Ark in the midst of a desert. But finally, it was done and all the animals had been loaded two-by-two, male and female. The dark wet clouds were gathering and there was a foreboding rumble of thunder in the distance. All that remained was for God to close the door and seal it. But at this very moment there was a problem. Mrs. Noah refused to come aboard. She was standing at the bottom of the gangplank, her back turned toward Mr. Noah holding her cat. It seems the argument had started about Mrs. Noah's cat. Now Noah already had two cats on board and had simply suggested she leave her tabby behind. Now you must understand that while it was Mrs. Noah's cat, the center of its affections was Mr. Noah. It was always fubbing against his legs or jumping into his lap hoping to be petted. We all know of cats like this, who have a fondness for men who can't stand them and never return their affections. Moreover, Noah knew her cat was quite a mouser and hunting could not be tolerated on the ark! There were only two mice! But Mrs. Noah's stubborness went far beyond the matter of that cat, as it became more and more clear..... "Come aboard Woman, its time to go." "No! I'm sick of this Ark - it has had all your attention for the past 100 years. Every time I have needed you - you've been off sawing gopher wood or nailing it together. I hope this Ark doesn't leak like the roof you never got around to fixing." "You know very well God told me to build it. Come aboard now, it's starting to rain!" "No! You love this Ark more than you do me! I have cooked for you and done your laundry and raised three boys singlehanded - Shem and Jephtah and Hamm especially has been quite a handful. You've been off building Your Ark in the middle of a desert. You don't even care that I'm the laughing stock of the whole neighborhood." "Get in here right now Woman, I need to save the world." "If you want to save the world, you can start by saving your marriage. You don't even like my cat!" A loud crack of thunder ("Noooo-aaah!") and a sheet of pouring rain made up Noah's mind as he grabbed her by the arm and dragged her aboard... "You Devil! Get on board and bring that lousy cat with you!" Now the Devil was hiding nearby just waiting for such an invitation and as Noah pulled his wife in, he changed into a large red rat with pointed ears and a forked tail, scampered aboard and disappeared quickly down into the hold bent on sabotage. The Lord sealed the door shut and the rains began. You know the story - how it rained and rained and rained for 40 days and 40 nights and covered the earth with a great flood in which all life perished except that aboard Mr. Noah's Ark. What you don't know is that while the storm raged ouside, a mostly silent argument continued with similar force within. And as the argument continued a sinister red rat bent on sabotage was gnawing and gnawing away at making a hole in the bottom of the ark. What few words were spoken between Mr. Noah and Mrs. Noah were icy and hard. The cramped conditions and all the work feeding and caring for all that livestock day after day for weeks didn't help either. Nor did the fact that Mrs. Noah's cat was constantly under Noah's feet. Its affections were harshly rebuffed again and again as it rubbed against his legs or tryed to sleep in his lap. Everything came to a climax when Noah tripped over the cat and fell into a pile of elephant dung that Mrs. Noah was shoveling out a port hole. Noah blew his stack, and the cat, realizing that she was not wanted, took off for the haven of the hold as Mr. and Mrs. Noah, finally pushed to the breaking point, cut loose on each other full force. As their angry words echoed down into the ark, Mrs. Noah's tabby came upon the red stowaway deep in the hold gnawing busily away and knew immediately what it was up to. Pouncing on the wretched rodent, the cat hurried off to to present its prey as a gift to Mr. Noah. As the cat approached them. Mrs. Noah was screaming something about "this Ark is no romantic cruise ship" when Mr. Noah spotted the cat with its prey in his mouth, and in a burst of sudden released fury, tossed it and its prey over the side. Mrs. Noah was screaming "My Cat! My Cat!" as they hit the water. The cat released the rat as she hit the water and the Devil returned to his original form and started swimming away, even as Mr. Noah realized what had really been happening. He might be saving the world, but that overly affectionate cat had saved his ark. Cooing words of apology and remorse to Mrs. Noah, he fished the cat out of the water with a net. At that moment, the sun broke through the clouds for the first time in many days and the cat sat on the step in the sun drying itself with a smug look on its face. And to this day, cats love to sit on their doorsteps in the sun, remembering how once a cat saved the world.