I have ...
* Seen two deployed biplanes damaged, although I didn't see what happened.
* A biplane intercept my biplane (that was bombing). Afterward, it re-based away.
* Jet-fighter bombing. I have so far never seen biplane or fighter bomb anything.
* Bombers and Jet-bombers bomb. They are reluctant to do it, but when they start, they bomb like there is no tomorrow. Very often they bomb a city even though it is already at zero defence. They also tend to like to do strategic bombings.
* Bombers nuked my neighbour. Twice. I have walked into nuked areas more than this, but this is the only time I saw it live.
The AI doesn't use them enough. It looks like they don't understand that unless there is enemy planes or flak nearby it is safe to use the planes every turn. This must change. I hope the dev fixes this. They also must fix so the AI build carriers and also when it comes to carriers, let the carrier have 1 xp for every mission the planes on it do. The AI must also start to deploy their planes. I have seen it, but only a couple of times.
On the other hand, most civ games had problems with some rules until the first couple of patches. Was it Civ 3 or was it Civ 4 that the intercept function didn't work at all (they didn't intercept anything) until they patched it. So there is hope.