I've never been asked for my credit card on checkin or boarding, nor have I ever heard of anyone I know being asked for one.
It would be extremely weird for such a thing to be asked for, as a lot of tickets (probably the majority) are not paid for with a personal credit card (or indeed any credit card).
A large percentage of traffic is business travel, purchased either through a corporate travel agent (using whatever payment method, most likely he's just billed once a month or so for all the traffic he sells), a company credit card, or a bank transfer.
Then there's the large volume of vacation travel using package holidays where the ticket is supplied again by the travel agent, who often buys it through several intermediaries. Again the traveler won't have information about how the ticket was actually paid for, nor would he have access to the payment mechanism if he did know.
And even if I buy directly from an airline, the airline usually has several payment methods, including bank transfer, credit card, and various others, and the credit card if used doesn't have to be the one of the passenger (you can buy a ticket for someone else).
In fact the only times I've ever heard it mentioned that people were supposedly asked for a credit card was in questions on this site where people wonder how to act if asked for a credit card on checkin because they've heard on the internet that strangers have been so asked...
My guess is the only time you'd ever be asked for your credit card is if there are problems with the payment of the ticket that show up on the checkin agent's screen, and then only if a credit card was used. Or maybe there's excess luggage that needs to be paid for, and the easiest way to do so is using a credit card.