The Black Arrow from The Hobbit. I haven’t read the books but is that thing magical or something? The 70s animated movie made it sound like a random arrow Bard just keeps finding after using. The live action movies turn it into one of many iron ballista bolts. But they both almost mystify the thing with how the characters are in awe over it.
Bearing in mind that “magical” items in Tolkien’s work are often not that dissimilar from ones that are just very old and very well made, The Hobbit mostly just hints at the idea that the arrow has any magical qualities. Really the arguments in favor of the idea come down to a brief statement made by Bard the Bowman about the arrow shortly before he uses it to bring down Smaug.
“Arrow!” said the bowman. “Black arrow! I have saved you to the last. You have never failed me and always I have recovered you. I had you from my father and he from of old. If ever you came from the forges of the true king under the Mountain, go now and speed well!”
But as for the reverence it receives, it is special to Bard because it is an heirloom of Girion, the last Lord of Dale, who was his ancestor. Plus there is the fact that it was more than likely crafted by the dwarves in the Lonely Mountain, so even without additional magical abilities it would almost certainly be a high quality item.
I suppose you could also give it special note as being the the weapon that ultimately succeeds in killing Smaug, but that has less to do with the arrow itself than the fact that Bard was told by a thrush where to find the only weak spot Smaug had.