In Civ V which tile improvements can be stacked with another improvements?

A land tile may have:

• A road or railroad (but not both)
• One tile improvement (farm, mine, trading post, lumber mill, fort, citadel, academy, custom house, etc - options depend on the tile type)

Tile improvements cannot be stacked, with one caveat - if a Great Person builds a tile improvement on a tile, it counts as connecting any strategic resources on that tile to your trade network. For instance, if you build a Manufactory with a Great Engineer in a tile that contains Iron, it will give you the Iron resource, even though Iron normally requires a mine. It does not give you the tile modifier of the improvement, though. So if you build a Citadel on Iron, you'll get the Iron, but not the mine production bonus.

This caveat is in the game because the strategic resources are not all exposed on the map at the beginning of the game. If you consumed a Great Person to build a tile improvement, and later that tile was revealed to have a critical strategic resource, you'd have to destroy the improvement to get the resource. This would waste your consumption of the Great Person.

Luxury resources are visible from the beginning of the game, so there is no such exemption for building Great Person improvements on luxury resource tiles.

Roads/railroads are the only improvement that can stack on another improvement without destroying it.

Building any of the other improvements on top of an existing one will destroy the original.

(If you want specific references, they'll have to wait until I'm on a network that doesn't firewall the wiki, sorry.)