In my opinion, there are two requirements for a good image/video when it comes to shooting aircraft: proper shutter speed, and great panning. In this lesson I will speak about the first, shutter speed.
First of all, the goal of anybody shooting propeller driven aircraft or helicopters should be to shoot at the slowest shutter speed possible so as to obtain a good amount of prop/rotor blur. A stationary propeller or rotor makes the subject look like it is just a toy, suspended in the air. An image with a full-disc of prop/rotor blur makes the picture pop with energy and excitement and more accurately portrays how the human eye sees it
When shooting propeller-driven aircraft, I suggest shooting absolutely no faster than 1/150 of a second. When I'm out of practice I will still shoot still photos at 1/125, but when I have been out shooting for days on end, I can handhold my 500mm lens down to 1/50 to get a nice, full, disc of prop blur. If your shooting jets you can certainly up the shutter speed, but keep in mind, tracking a fast subject with a completely stopped background is not nearly as exciting as one with a tack-sharp subject and a completely motion blurred background. When shooting jets I tend to keep it around 1/200. That keeps my autofocus happy, and it provides a nice amount of blur. Helicopters are the tricky buggers! Those you absolutely want to shoot as slow as possible, as the main rotor blades move much slower than propellers. Those you want to shoot under 1/100 second when at all possible.
While shooting video I am able to get a good amount of propeller blur when I select a shutter speed of 1/100 second. Sometimes, if I do not have to pan a lot, I will slow it down to 1/60.
Equipment consideration: slow shutter speed may make it more difficult for your cameras autofocus to track the subject! As I hinted above, there are very few times I will slow it down to 1/60 second using my Canon HG20 due to the fact that any slight shaking or movement of the subject will cause the autofocus to get confused.
Enjoy these tips and be sure to comment if you have any questions or need clarification! Eventually I hope to turn these into video tutorials.