It would really depend on the fare rules of your ticket. If you are on a fare that allows some changes/refunds, and you contact them before the flight leaves, you might be able to be re-booked. At the other end of the spectrum, if you are on a non-refundable, deep-discount ticket and you overslept and the plane left without you and you didn't contact them before departure, then you might just have to buy a new ticket.

If you have the chance you should always contact the airline before the flight leaves, even if you know you can't make it, and let them know your situation so your ticket doesn't automatically cancel. Then get to the airport ASAP even if your flight has left, and usually they will try to help. I think you'll get better assistance when face-to-face with an agent than over the phone.