It's the last day to book a flight on Southwest Airlines without being hit with a fee to check bags after the airline abandoned a decades-long luggage policy. Southwest Airlines will start charging many of its customers a fee to check bags beginning on Wednesday, abandoning a decades-long practice that its executives once described as key to differentiating the budget carrier from its rivals. The airline announced the change in March, saying at the time that the the new policy would start with flights booked on Wednesday.