Wood

Wood was an organic material deriving from trees. This was a widely-known fact. (TV: City of Death) "Woods" was also a word used to describe forests, spaces with large quantities of trees.

Wood would catch fire under extreme heat. (TV: The End of the World) Some objects that were made of wood, such as cricket bats, required regular application of linseed oil for proper maintenance. (TV: Castrovalva) Beavers could chew through wood. (PROSE: Wetworld)

The Doctor's sonic screwdriver was ineffective on wood. He was rather embarrassed of this. Once, when the Eleventh Doctor was battling Androzani trees, he complained about the aliens being made of wood, rendering his sonic useless on them. He again found himself in this predicament when facing peg dolls. (TV: Silence in the Library, The Hungry Earth, The Doctor, the Widow and the Wardrobe)

When trapped in the Tower of London in 1562, the War Doctor devised a plan whereby his sonic screwdriver could disintegrate the wooden door, using the added processing power of the Tenth and Eleventh Doctor's sonic screwdrivers, running a program for hundreds of years. The problem was solved, but application of the solution was interrupted when Clara Oswald walked in through the unlocked door. (The Day of the Doctor)

Many of his companions ridiculed the Doctor for his TARDIS exterior being seemingly made of wood. (TV: Smith and Jones, Meanwhile in the TARDIS, The Bells of Saint John)

Uses

Wood was often used to start and/or maintain fires either in a fire pit (TV: Countrycide, The Sound of Drums) or in a fireplace. (TV: The Girl in the Fireplace)

Books, gallows and spoons were all made from wood. (TV: Silence in the Library, Mona Lisa's Revenge) Doors were also made from wood. (TV: Silence in the Library, The Hungry Earth) One of Banquo Manor's doors were described as having been made of "strong wood." (PROSE: The Banquo Legacy)

Centuripedes required oak wood to build a pod to transport their eggs. (TV: The Last Oak Tree)

The Daleks had wood used as support beams in the mines dug by their human slaves during their invasion of Earth in the 22nd century. Ian Chesterton jammed the Daleks' bomb in its shaft with some left-over support beams, ultimately resulting in the destruction of the entire Dalek invasion force. (TV: The Dalek Invasion of Earth)

A wooden Cyberman was used during the Siege of Trenzalore in an attempt to bypass the Papal Mainframe's force field. The plan nearly succeeded since the Cyberman was low-tech but the Eleventh Doctor used his sonic screwdriver to send a signal which would have reversed the polarity of the Cyberman's weapon causing it to fire backwards. The Cyberman turned its weapon around and shot itself, since the Doctor did not mention the screwdriver did not work on wood. (TV: The Time of the Doctor)

References

When Amy Pond asked if a door would keep Prisoner Zero at bay, the Eleventh Doctor sarcastically retorted, "It's an alien multi-form from outer space; they're all terrified of wood!" (TV: The Eleventh Hour)