Isildur was the oldest son of Elendil. He defeated Sauron by cutting off the finger that bore the One Ring in battle, using the broken sword Narsil. He claimed the One Ring but was betrayed by it in the end. The Kings of Arnor (and eventually Gondor, as told in The Lord of the Rings) are often referred to as the Heirs of Isildur.
Isildur was born in 3209 of the Second Age in Numenor. His first action of note was when he stole a fruit from Nimloth, the White Tree, after the King (who was corrupted by Sauron) ordered that it be cut down. He was badly injured but successful. Later he escaped the destruction of Numenor with his father and the rest of the Faithful.
In Middle-earth, Isildur and his brother Anarion founded Gondor. Isildur personally established Minas Ithil and Ithilien. When Sauron captured Minas Ithil, Isildur fled Ithilien by the Anduin. He then met Gil-galad and Elendil in western Middle-earth.
When the Last Alliance of Elves and Men marched on Mordor in 3434 SA, Isildur was among them. They laid siege to Sauron for seven years, until Sauron himself came out to fight. After Sauron killed Gil-galad and Elendil, Isildur cut the Ring off his hand with the hilt-shard of Narsil, his father's sword. Sauron was greatly weakened, and fled in spirit form to Mirkwood. Against the advice of Elrond and Cirdan, Isildur took the Ring, deciding it would be a weregild for his father and brother.
After the defeat of Sauron, Isildur spent some time in Gondor, where Anarion's son was established as the leader; after this he left for Arnor. He wanted to take counsel with Elrond on the matter of the Ring; also some of his family had stayed in Rivendell. Unfortunately on the way, he was attacked by Orcs. When he tried to escape by putting on the Ring and fleeing in order to keep them from taking it, the Ring slipped off his finger, and he was killed.
In Movieverse Edit
In the movies, Isildur is referred to as the last king of Gondor. It is not known if this was simply a mistake or a purposeful change. Anarion and Arnor are also not mentioned. Unlike the book, he is brought to the Cracks of Doom before refusing to destroy the Ring; in the book he was simply advised to do so.