It may stand to reason that I don't want to build on top of Mt. Everest, but I do want to build a nice city like Denver, which is basically on the side of a mountain.
All kidding aside, this thread stems from the way I have carried over my cookie cutter city placement from every rev of Civ, so as to maximize the amount of terrain a city can put into production. Unfortunately, in Civ III, about 25% of the time one of those darn mountains is taking up the square where I want to build my city!!! I'm sure I'm not the only one that places every city three diagonal squares and one square over from the last city that was built.
If someone from Firaxis reads this.... please *please* !!PLEASE!! allow terraforming of mountains, or placing of cities in mountains in future patches!
As far as terraforming mountains, it could easily be a build option granted to workers by a technological advance, perhaps Ecology.
As far as mountain cities, we have plenty of them in real history. Besides Denver, look at the ancient cities on the Tibetan Plateau or in the Andes Mountains, like Macchu Picchu.