Chop out your second worker and settler from the capital.
Also chop out your early worker/settler pairs unless you can
make a settler factory by having a city with a large food surplus.
I'm also not afraid to chop trees for barracks, granaries, libraries, and wonders.
Chop courthouses in newly conquered cities.
I generally leave trees on plains, and chop trees on grassland.
The exception: I also chop trees on hills and rivers. By the time lumbermills roll around, I can usually employ them around the AI cities I've conquered by using my own forests to fuel the fires of industry...