1. When involved with campaigns, use bombers to destroy all roads on tiles with resources (strategic and luxury) first. This way, the AI's cannot manufacture the really cool military units, and the reduction in luxury will increase unhappiness, crippling their economy.
2. Use bombers to reduce hitpoints to 1 for all defensive units. It will make it so much easier for your mechanised units to take a town. Make sure that you also engage in carpet bombing in order to reduce the population of the cities to less than 7, after which they become towns and loose all defensive bonuses.
3. On higher levels, you need air supperiority missions to keep the AI at bay.
4. Artillery can only move one tile per turn on enemy territory. Planes do not have this limit, which means that fast moving units (3 movement points) can reach and capture enemy cities much sooner (compared to softening cities when using artillery and moving them one tile per turn).
5. The best thing about planes is that in one turn they can reach any friendly city on the map!!!!! You can shift your military focus in one turn (as opposed to 8-10 turns in Civ2 since you could only move 8 squares per turn).
6. In retrospect, once I discover flight I no longer produce artillery units.