I am a former Delta flight attendant (and aunt to 3 toddlers), and always recommend that parents use carseats for their kids on the flight. Unfortunately, the government does not require the use of carseats on airplanes, which makes many parents think it must be okay not to use them. That is just not true.
Most parents who would never dream of driving around in their car without putting their precious children in car seats. But, they get on a plane, which goes @ 200 mph on the ground, and the carseat suddenly seems unnecessary. If the pilot has to slam on the brakes during takeoff or landing going 200 mph, a child is not safe in a lap or in the lap belt.
I know that many parents are just trying to save money by keeping the child under 2 on their lap, but your child's life and safety are worth the few hundred bucks. What really surprised me was the number of parents who actually paid for a child's seat, but didn't bring the carseat onboard.
Please, for the safety of your own children, use a government approved carseat on the airplane.