In the movie version of The Lord of the Rings, Legolas is seen many times shooting arrow after arrow, yet he never seems to run out.
For example, after the long battle at the end of The Fellowship of the Ring, his quiver is completely filled.
Where are all these arrows coming from? Is it some form of elven magic? If so, it is never explained either in the movie, nor in the book that I can recall.
This might be true in the movie, but certainly not in the books. Twice - in the very battle you mention at the end of Fellowship, and again in the battle of Helm's Deep - he is explicitly described as running out of arrows and having to hunt around for more:
'And I,' said Legolas, 'will take all the arrows that I can find, for my quiver is empty.' He searched in the pile on the ground about and found not a few that were undamaged and longer in the shaft than such arrows as the Orcs were accustomed to use.
...
'Two!' said Gimli, patting his axe. He had returned to his place on the wall.
'Two?' said Legolas. 'I have done better, though now I must grope for spent arrows; all mine are gone. Yet I make my tale twenty at the least. But that is only a few leaves in a forest.'
(And yes, he does later go on to use a knife, saying to Gimli: "It has been knife-work up here.")
On a side note, I've always found this set of exchanges between Legolas and Gimli to be faintly disturbing. Although Orcs are "evil", and their enemies in this battle and the wider war, they are still sentient creatures and I would have thought Legolas - as a "good" Elf - would at least show some form of regret at the necessity to slaughter them. But instead, he revels in it and turns it into a competition with his friend. As I say, disturbing.
In the movie, at the Battle of Helm's Deep, Legolas is seen using two knives instead of his bow and arrow. One might presume that he ran out of arrows. I recall reading in the LOTR wiki that Legolas does indeed run out of arrows, and when that happens he has two knives that he uses as weapons.
From the Lord of the Rings Wiki:
Legolas carries two weapons with him on his journey with the Fellowship. He sports a slender bow of Mirkwood which he aims with deadly precision. He prefers to pierce his enemies from afar, but he also carries a long knife of unknown make. In Lothlórien he was given a bow of the Galadhrim, stouter than those of the fashion of Mirkwood. Nevertheless he adopts his new bow and makes deadly use of it in the remainder of the War of the Ring. Legolas' skill with the bow is reknowned, perhaps even comparable to that of Beleg Cúthalion.
In the movie adaptation he wields an additional elvish long knife.
(Lord of the Rings Fandom page - Legolas:Weapons, archived version from 2012/02/08)
