Elendil used Narsil in the Siege of Barad-dûr and, being slain in combat with Sauron, fell over it and broke it. Isildur took it and used its shard to cut the One Ring off the hand of Sauron (who had also fallen). After the death of Isildur in 2 TA the shards where taken to Rivendell.
In 3019 TA Narsil was reforged as the sword Andúril and given to the heir of Isildur, Aragorn.