I'd bomb anything with them, except cities. I don't like how they would target anything, units, population, or improvements. I especially hate when they destroy markets.
I guess many players already know this, but for those few who don't know, and like to use bombers, here's an advice:
If you build a bomber in a city and want to move it to attack from another city, you have to relocate it. By doing this the bomber misses its turn. Well, you can set the rally point of the city building bombers to wherever you want it to be relocated. This way at the beginning of the turn, just out of the factory, it will be relocated and won't miss its turn. Don't know if you can set the rally point to a city in another continent... I'll try that next time I want to use bombers. But in case you can't, you can still set the rally to a coastal city, load it in a carrier, and transport it across the sea to the destination continent. If it is close enough, the bomber can be attacking from a remote city in a distant continent the same turn it was built!
Edit: yes you can! I just remembered doing that not long ago with stealth bombers, setting the rally point to an island across the sea, appart from the main continent. So you could build an airfield in a remote empty island, and have your bombers attacking from there the same turn they were built.