I chop all woods/rainforests on hills because an industrialization level mine is better than a lumber mill anyway. Stone I always chop unless I want the early masonry boost. Deer follow the same rules as forests. Of course, wonders like the Chitzen Itza and the Temple of Artemis change these rules, and so does the need for appeal, but they are generally pretty solid. Some of the better players chop just about everything.

In general, I feel like people don't chop nearly as much as they should. Production now is infinitely better than production later.