Clear Airfares Act of 2009 - Makes it an unfair or deceptive practice for: (1) a domestic or foreign air carrier or ticket agent to sell an airline ticket without simultaneously displaying all applicable ticket taxes, fees, charges, and surcharges in reasonable proximity to the price of the ticket (including on the Internet to an online purchaser); and (2) a domestic or foreign air carrier to impose a fuel surcharge that is not correlated to the price of fuel paid or the amount of fuel used by the air carrier on the specific flight.