Does Frodo die in the third 'Lord of the Rings'?

If you really must know, here's what happens in the book. Frodo is about to throw it into the fire and destroy the ring, but he succumbs to its power and just like Isildur, does not destroy it. Out of nowhere, Gollum grabs a hold of Frodo's arm and tries to take the ring from him. He bites Frodo's finger off, along with the ring. Gollum is so happy that he starts to dance and jump and loses his footing and falls into the fire, thus destroying him and the ring. Later, the injured Frodo and Sam are rescued by the Eagle King from the side of Mount Doom.

In the book, Frodo survives, but is permanently psychologically scarred by the experience. He is never able to rest in this world and goes with the elves across the sea to a better place.

The first Lord of the Rings film was very true to the book. It left out certain scenes, but was essentially the same as the book. The second film, the Two Towers, took more liberties with the plot, introducing extra scenes, changing people's motivation and so on. It is possible, but unlikely, that Frodo will die in the third film.

No, Frodo does not die in the third installment of 'Lord of the Rings: The Return of the King' in either the book or movie. He does not even die while standing over the lava of Mount Doom because the power of the ring takes a hold of Frodo, for it easily tempts anyone.

Take for example Isildur, when he and Elrond are in the same position. As Gandalf forshadowed, "Even Gollum may have something yet to do." Gandalf was quite right, Gollum and Frodo both want the ring, Gollum desires it so much he bites Frodo's ring finger. He then is so delighted he dances and falls off by accident, therefore destroying the ring.

Then Gandalf and the eagles fly to Mount Doom and save him and Sam. Frodo returns and finds the memories of the Whethertop where he was stabbed and the ordeal that the burden of the ring took on him was too much pain.

Arwen who did not go to the Grey Havens, also referred to as the undying lands, stays with Aragorn as queen of Gondor. Frodo takes her spot on the last ship to the undying lands with Bilbo, Gandalf, Galadriel and her husband Celeborn and finally Elrond. They go to a place away from despair and grief, where Frodo can heal.

Upon his return to the Shire, Frodo helped clear out a criminal mob, led by his cousin, Lotho Sackville-Baggins, and the fallen wizard Saruman, that had taken over the region during his absence. He refused to draw his sword, however, and saw to it that any enemies captured were not killed. He never recovered from the physical, emotional and psychological wounds he had suffered during the War of the Ring, and was in particular taken ill on the anniversaries of his wounding on Weathertop and his poisoning by Shelob. He briefly served as Deputy Mayor of the Shire, but later resigned. Two years after the Ring was destroyed, Frodo as the Ring-bearer and Bilbo as the Ring-finder were accorded the special right to travel to Valinor — where Frodo might be healed and find peace — together with Gandalf, Elrond and Galadriel, the Keepers of the Three Rings. They boarded a ship at the Grey Havens and passed over the sea. Having no children of his own, Frodo left his estate, along with the Red Book of Westmarch, to Sam, who, according to Hobbit legend, followed Frodo across the sea sixty-one years later, following the death of his wife Rose (née) Cotton.

https://en.wikipedia.org/wiki/Frodo_Baggins

Read the book for the best answer, but no, he doesn't die.