Is it possible to cancel or refund a plane ticket that has been booked?

That depends. Non-refundable airfares are much cheaper then refundable ones. If you cancel or change flight on these, you will pay a fee. If you are booking in the US, and as long as you booked a non-refundable ticket 7 Days before your flight, you don't have to pay a fee for a window of 24 hours to cancel or change a flight. Hope this helps.