You can probably guess that a digital SLR is going to give you better results than a point and shoot--but you can still get good photos with even a compact camera. The catch is that you need a long telephoto lens (generally at least 300mm) to fill the frame with passing aircraft. If you're using a compact camera with a top zoom of 120mm, most of your photos will show a big blue sky with tiny airplane-shaped flecks in them.
Even so, wide-angle lenses can come in handy for capturing aircraft on the ground--called "static displays" in airshow lingo--and crowd shots. I typically bring my trusty 18-200mm zoom and a 400mm telephoto. And as you see here, shots of planes on the ground can be fun.