Time for some airplane porn: Lockheed Martin has completed high angle of attack testing for the F-35A Lightning II. The aircraft was able to get to its 50 degree limit with ease:

F-35A test aircraft are limited to AOAs of 20 degrees until their controllability is proven at a higher AOA limit of 50 degrees. The ability to rapidly progress to the maximum AOA indicates a sound aerodynamic and flight control system design. High AOA testing will continue on the F-35A for several months testing the capabilities of all design loadings and the flight control system.

Being able to fly at a high angle of attack increases the airplane's maneuvering abilities, which is crucial for dog fighting. One extreme example is the cobra maneuver (also known as Pugachev's Cobra), in which the plane suddenly lifts its nose up while maintaining altitude. This reduces its speed considerably, which could make a pursuing enemy to overshoot, giving the pilot a window of opportunity to fire at it.