The uncle of Éowyn and Éomer, Théoden was misled by Gríma (or Wormtongue as most others in the Mark called him). Théoden initially rebuffed Gandalf's advice, but after being healed by him he led the Riders of Rohan into battle at the Helm's Deep and the Battle of the Pelennor Fields.
In that battle he challenged the Witch-King of the Nine Ringwraiths, and died when his horse Snowmane fell upon him after being spooked by the Ringwraith's flying beast. He was immediately avenged by his niece Éowyn and the Hobbit Meriadoc Brandybuck, both of whom had ridden to war in secret.
The name Théoden seems to be derived from the Old Norse word 'þjóðann' meaning "king".
In the 1981 BBC Radio 4 version of The Lord of the Rings, Théoden's death is described in song rather than dramatized conventionally, which tends to lessen its impact.
Peter Jackson's film The Lord of the Rings: The Two Towers (2002) deviates from Tolkien's story by having Théoden (played by Bernard Hill) actually possessed by Saruman rather than simply deceived by Gríma.