If I should happen to hand you a debit or credit card that simply does not scan in your reader even when swiped correctly, please do not look at me with a hangdog expression and say "Oh, it didn't scan, do you have another card?" The card has numbers clearly printed (embossed, even) on the front of it, which are in fact the same numbers embedded in the stripe. Your till has a keypad and so does the card terminal when it's a separate item. TAKE THE EIGHT SECONDS AND KEY IT IN MANUALLY, just as you'd do for a phone order. In the time it takes you to ask and me to fish out another card or cash, you could be done already. If it declines, then I'll give you another card. (You do know that in days of yore, prior to about 1990 or so, there WERE NO card readers, right? It was all carbon copies and telephone calls.)
I worked a cash register for 2 years and I never asked a customer for another payment method because of a scan issue. Swipe once; if it doesn't read, try again; if it still won't go, key it in.
Edit: I honestly had no idea any store had a blanket policy forbidding manual input. None of the ones I worked at did (all of them took phone orders of some sort; that might be part of why) and such a policy is one of the stupidest things I can imagine a store inflicting on its customers and employees (it might even be against their contract with the card brand, because it could be seen as tantamount to refusing that card). However, assuming that were the case in any particular instance, it would be easy to say "I'm sorry, this didn't read <i>and we aren't allowed to key manually</i>, do you have another card?" Instead I always just get a dumb look. It's a minor thing but it plays out the exact same way just about every single time, so it gets annoying after awhile.
The card damage thing is because I've seen readers that have a stop at one end of the card slot so that you can't swipe it in that direction, but some cashiers swipe it that way anyway and slam the card up against the stop.
Another reason I get irritable about this is because I have two cards that are cracked that I use at self-serve POS terminals. One has the stripe completely cracked in half and taped back together; on the other, the top half of the stripe is hanging by a thread. Rarely (never at a swipe terminal or ATM and only a few times at an insert-card ATM) have either of them failed to read on the first attempt when I swipe them correctly. And the ones that don't read them just don't, no matter what tricky maneuvers you try to pull, so there's no point to wasting time trying.