The climactic dogfight with the MiGs. Especially during the part where Maverick overcomes his Heroic BSOD at the beginning of the dogfight when he nearly goes into a flat spin that caused Goose's death halfway in the movie and Maverick dodging a MiG by braking then blowing him away with one last missile.
Meta example: During shooting Tony Scott needed a specific shot and was told by commander of the aircraft carrier that it would cost $25,000 to turn the carrier and get it. Scott broke out his personal checkbook. He got the shot.
The aerial cinematography as a whole, which is still stunning to this day. This is a movie that could easily be done with CG substitutes in this day and age, but there's something awestriking knowing you're watching real fighter jets the whole way through.
The Fighter Launching Sequence in the opening deserves a mention. The entire intro is basically a love letter to the F-14A Tomcat, with amazing shots of the carrier crew prepping the fighters for launch, and then as the engines light up Danger Zone kicks in.
A corollary to that is the awesomeness that was the Grumman F-14 Tomcat. A carrier-based supersonic interceptor with the most advanced avionics and weapons of the time, including the AIM-54 Phoenix missile system. The workhorse of United States Naval Aviation, it served until retirement in 2004, providing fleet interceptor protection as well as being modified for ground-attack roles in its latter years.