Let's hear everybody's witty retorts to this common question and I'll collect them into a FAQ. C'mon, everyone has at least 17 of these. Thanks for you contribution to this important work. Here's what we have so far:

"Same thing that happened to her legs."

"There's a reason you're supposed to face the door in an elevator."
"Details, details."
"He used to belong to some farmer's wife. He doesn't look much like a blind mouse to me, either, but it happened..."
"Don't ever run after a farmer's wife if she's got a carving knife."

"It got caught in the cat door."
"I used to grab her by the tail and swing her out the door, and one day it fell off."
"They charge extra for tails."
"She was chasing her tail. She caught it."
"We used to have this really powerful leaf blower..."
"It got curtailed." [This is an ancient, notorious pun about the Dog Watch in the British Royal Navy, which is half as long as a regular watch to accommodate supper.]
"Well, you've heard of Ox-Tail Soup?"
"I come from northern Minnesota. 'Cold enough to freeze your tail off' is not just a figure of speech."
"It got caught in the CDRW loading tray, and and you know the little laser inside that burns the CD.....?"
"There's a reason why he runs from the vacuum..."
"What do you mean? It's right there!"
[Looking at nub in feigned surprise] "OMG! It's gone!"
"Well, see, we went up this escalator..."
"She only wears it for special occasions."
"Oh gosh, we left it at home with his stilts.."
"She checked it at the door at a party and forgot to pick it up."
"His brother chewed it off...just like his legs and his collar. I hate when that happens."
"Well, my nephew was running with scissors..."
"We taught the kids never to stick their fingers into electric outlets or empty light-bulb sockets, so ..."
"There's a reason she doesn't chop wood with me anymore..."

"There was this dog, once, wandering around a railroad yard -- keeping an eye and ear open for moving trains -- one day a SWEET little bitch came strutting by, and he was smitten to distraction and didn't hear the train coming. As the wheels ran right over his beautiful tail, he whirled around, realizing his mistake too late, and BAM! his addled little head smacked into the side of the train. Poor guy. This is what's known as losing your head over a piece of tail."

"Losing it was the price for joining the Yakuza. Don't mess with these dogs."
"She's a rescue; used to live with a butcher who ran a sausage shop..."
"He lost it in a poker game."
"They shed their tails every year, like deer shed their antlers. They take about 6 months to grow back."
"Same thing that happened to my tail."
"She was born without one, so we bought her this lovely fluffy tail from our friend the nice Gypsy lady -- it cost a lot because it's a magic tail that only quality people of discernment, good taste and virtue can see."
"She was off cadging treats when they were passing them out."
"They don't need tails; you pick them up by the ears."
"She ran her tail off doing agility."
"I pulled so hard on his ears when he was a puppy, that I pulled his tail in."
"She kept wagging it in front of the TV."
"It kept getting caught on my watch."
"I forgot to put it back on last time I used it for a duster."
"He heard the old cliche' about 'the **** hitting the fan' and thought it would be a fun April Fools' Day prank. Unfortunately, his tail hit the fan. Hoist on his own petard."
"Shark attack".
"Unknowingly, we took her to a stoned dog groomer; told him to comb her fur and cut her NAILS."
"Don't slam doors."

I know it's out-of-fashion, but we could actually tell the TRUTH:
"Corgwyn are a gift of the faeries, whom they served as steeds and companions. Long ago, the corgwyn rebelled against the faerie queen, who fastened their tails to the ground as retribution; not to be dominated, these plucky creatures gained their freedom by pulling so hard that their tails broke off. Since then, their service to the faeries has been voluntary. But they have no tails to this day."

Thanks everybody, keep them coming.