Halo 2 > Halo 3 > Halo 3 ODST > Halo Reach > Halo CE
Based on campaigns.
Here is a way I found to get a banshee on The Covenant
1. Grab a hornet and advance as normal. Kill the anti air wraiths, the shade turrets and the wraith.
2. This is were timing is important. Wait until the green phantoms drop off the elites. When a banshee is flying over a green phantom, shoot it softly with the machine guns, preferably from behind, so that the brute dies and the banshee doesn't
3. The banshee should land on the green phantom if the timing was correct. Now, exit the hornet and land on the phantom, and then take the banshee
4. You're done! The only thing is the banshee may be a little damaged, but aside from that everything should be fine. Now just use the banshee for whatever you want. Personally I find it fun to splatter all of the brutes guarding the tower.
So there's how you get a banshee on The Covenant. The only negative thing about this is that the banshee de spawns later on. If you have a quicker method of getting a banshee on The Covenant please post it :)