Ace Combat
The Ace Combat line of PS2 games is the most popular flying series for the console. There are a total of five in the series, not to mention spin-offs. The top rated is Ace Combat 4: Shattered Skies, in which you pilot the fastest and most powerful aircraft through 24 missions.
Lethal Skies II
Ace Combat 4's main competition is Lethal Skies II. Its physics engine is more accurate than Ace Combat's, as it will not allow you to do feats that are impossible in the real world. The game spans 20 missions that include hunting for submarines and getting into dogfights.
Aero Elite: Combat Academy
In this flight simulator, you learn flight maneuvers of more than 60 types of aircraft, including helicopters and jumbo jets. You can also battle flying enemies using several different combat systems. The primary focus of the game is combat, as the fighting systems are more accurate than the physics.