This is something I'm having a lot of trouble with in Civ4. It seems like for most of the game, it's best to just leave forest tiles alone. I mean, if I cut down a forest to build a farm, I gain food but at the expense of production. And if I cut down a forest to build a workshop, I gain production but at the expense of food. In the end, two forest tiles net me the same food and production as a pair of tiles with a farm and workshop - except the forest is there from the beginning. In addition, forest tiles provide a health bonus!
Now I know later in the game techs increase farm and workshop output, but likewise there are techs which increase forest output (lumbermill), so the point seems mute. In fact, the only situation in which I can see removing forests would be beneficial, is if a town has an over-abundence of hills/minerals or floodplains/fish/livestock and you need to balance the food/production out. But having a town in that kind of situation is the exception and not the rule, and most towns provide enough forest tiles to give you that balance from the get go.
Now I know later in the game techs increase farm and workshop output, but likewise there are techs which increase forest output (lumbermill), so the point seems mute. In fact, the only situation in which I can see removing forests would be beneficial, is if a town has an over-abundence of hills/minerals or floodplains/fish/livestock and you need to balance the food/production out. But having a town in that kind of situation is the exception and not the rule, and most towns provide enough forest tiles to give you that balance from the get go.