Airbus
Airbus was founded in 1970, and started making planes in 1974, when the Airbus A300 was debuted. Other planes that they have made are the A310, A320 series (A318, A319, A320, and A321), A330, A340, the newest addition to the fleet, the A350, and the famous, double-decker, A380. Airbus began incorporating more high-tech features in the A320, with a fly-by-wire system.
Boeing
Boeing is the grandpa of aerospace engineering, founded in 1916. They are known to have the largest factory in the world. Their commercial planes include the 707, 717, 727, 737, 747, 757, 767, 777, and the new 787 aka Dreanliner. Boeing's most sold plane is the 737, while their most famous is probably the 747. The Air Force One is also a modified Boeing 747.