Théodred, only son and heir to King Théoden of Rohan, fell at the Battle of the Fords of Isen in the War of the Ring. A squad of elite troops, ignoring heavy loss, charged Théodred, slew his guard of knights, and killed him.
This was part of a strategy by Saruman (now corrupt) to hold King Théoden completely under his sway. In tandem with the planting of Gríma Wormtongue, a scoundrel/spy very close to Théoden, this strategy would have worked to a tragic end. But, as related in The Lord of the Rings, several members of the Company of the Ring (specifically, Gandalf, Aragorn, Legolas, and Gimli) arrived soon after the battle and helped save Théoden from the evils that surrounded him.
The result was fatal. Had Saruman not made it such a heavy priority to assassinate Théodred, his armies may have won the fords of Isen much more quickly, and arrived at Meduseld before Gandalf. If so, Rohan would not have answered the Red Arrow, and Gondor would have lost the Battle of the Pelennor Fields. Furthermore, should Frodo finally destroy the ring, the other members of the Fellowship would probably have been dead - including Elessar, the surviving heir of Isildur.
However, it was not so. Isengard was destroyed, the Rohirrim, thanks to the Ents, were victorious at Helm's Deep, and Saruman's staff was broken. Théodred was slain, but Éomer Éadig, Théoden's sister-son, would inherit the throne, beginning the Third Line of Kings of Rohan.