Wood is a common material for items to be made from and is commonly vulnerable to the element of fire and also acid in games where it is present. Many weapons are at least partly wooden, and magical staves, wands, and rods may also be of wood. Shields are typically made from wood, although shields of metal are not uncommon in roguelike games. Other wooden items may be encountered. There are many types of wood, with different properties. Few, if any, roguelikes have attempted to use multiple types of wood. Magical wood could have very unusual properties.
Dungeon doors are typically made of wood, often reinforced in some way. If a character can build a fire in a game, it will almost certainly involve the use of wood for fuel, if the need for fuel is not abstracted away. A game that allows a character to build items will likely allow items to be made from wood. It is in this kind of game that different types of wood really become useful. You need to find an appropriate (or exceptional, if possible) wood for the type of item you want to make. A bow has different needs from a bridge or a barrel.