Sky Rogue shows beautifully how the genre can be explored. You can choose between several markedly different planes, and scenarios include fighting against stationary targets, other aircraft, and massive airships, the latter of which often include sub-targets, such as turrets.
Weapons also offer a lot of ways to make your gameplay feel good. In addition to simple weapons, you could also include multi-stage missiles, lasers, or any kind of contraption you can think of.
Go check it out!