When buying plane tickets online using a credit card, keep in mind that some airlines will ask to see said credit card before checking-in at the airport. If you fail to show the card, boarding will be denied.
When booking online you are likely to be told at some point: it may be during the booking precess, or it may be written on the confirmation e-mail that you receive after booking (make sure to read the small print).
If you want to be sure, go to the Terms and Conditions page of the airline you're flying. Press Ctrl-F and search for "Card", to read their policy regarding this matter.
When booking you may be asked if the person paying is also flying. If someone else booked and paid for your flight you may get away with it by showing a copy of the credit card (both sides) used to buy the tickets, along with a copy of an ID and a note from the owner acknowledging the purchase. If you by the tickets for someone else, you may want to provide those documents for them.
It's a good idea to have a copy (both sides) of your credit card with you. If your credit card expired, you may want to keep it and bring it with you at the airport.
If for some reason you think you may not be able -or will not be able- to show the original credit card used to purchase your tickets, you should contact the airlines as soon as possible before the flight. They will be able to tell you if the credit card will be needed or not, and what to do in your particular situation (lost credit card, someone else booked for you...) You can also do this preventively and contact the airlines before booking, or book through a travel agency instead.
These are some of the airlines that explicitly say in their Terms and Conditions that they require you to show the credit card used to buy the tickets (if you bought them online from them).