Can you disband a city that you have chosen not to disband when given the choice?

Simply, can you destroy one of your own cities?

Nope. Only way to maneuver around this is to gift it to someone you want to decalre war on and then take it and burn it.

You could also delete it from the world builder

yeah but thats H4X

I actually delete alot of roads in freshly acquired territory using worldbuilder since you cant pillage your own roads either for whatever reason. What I do if you want to avoid 'cheating' is grab a post-it note, or any piece of paper that is around 3" x 3" and put it over the minimap so you don't accidentally see the map you haven't explored. Then zoom in real close to the city then enter worldbuilder and delete the city. Then exit. It's not a great alternative but it works.

Yeah, you can di alot with worldbuilder. But still, it's seems weird when you have to "cheat" or "moderate" the game to delete som of your own buildings. In a game like Civ IV you should be able to destroy buildings and improvements through the city screen. Now, I'm not talking about deleting core buildings like palace, but buildings like factory and such. If you think about it, in reality many cities have gone from industrial to commercial ones.

PS. You should also be able to desert cities of low importance, but all of this is just my opinion... ;)

In the early game, you can simply leave it undefended and let the barbarians take it. This is usually what you should do if you have conquered a continent with a chariot or quechua rush.