Summary
The Lord of the Rings trilogy is such a massive epic that there were inevitably going to be some serious cuts to the original text in any adaptation of it. This includes Peter Jackson's filmed trilogy, which, among other elements, completely exorcised the character of Tom Bombadil and the effect he had on the story.
While this has remained somewhat controversial among the fandom, Tom has steadily become more recognized due to the cuts made for the film adaptations. But there's actually a long-standing fan theory of the original books, which, if true, quietly means Tom Bombadil was in the movies all along -- in his true form, the Witch-king of the Nazgûl.
How the Witch-king Could be Tom Bombadil in the Movies
The theory -- which was first posted in 1996 and can be found in further detail at Flying Moose -- suggests that Tom Bombadil is actually a disguise for the Witch-king, the leader of the Nazgûl. Sauron's wraith champions are some of his most powerful figures, with the Witch-king, in particular, being powerful enough to contend with the likes of even Gandalf. The theory argues that Tom's overall lack of notoriety in the books is because he's primarily a disguise, giving the Nazgûl leader a means of traveling incognito.
The Ring having no effect on Tom could be the result of his Ringwraith nature, and his ability to see Frodo even while he's invisible and wearing the Ring gives him a similar skill to the Witch-king -- who could still see Frodo even when he tried to hide on Weathertop by using the Ring. The theory argues that the wight Tom saves the Hobbits from was actually one of his own, seemingly luring the Hobbits to the Prancing Pony -- where the Nazgûl later stage an attack that might have succeeded if it weren't for the intervention of Aragorn. The biggest hole in the theory is the existence of Goldberry, but she could either be an illusion cast by the Witch-king or an unassuming civilian unaware of her husband's true form.
It's an interesting theory that could explain a lot of Tom's peculiar eccentricities. The form would make him susceptible to Sauron's will, explaining why people like Elrond and Gandalf are hesitant to give him the One Ring. His memories of a long-lost kingdom could be a reference to Angmar, the long-lost realm once ruled by the Witch-king when he was still just a man. It's an intriguing concept at least and, if true, means that a live-action Tom Bombadil was in The Lord of the Rings films after all.
The Lord of the Rings' Tom Bombadil, Explained
Within the Lord of the Rings fandom, Tom Bombadil remains one of the franchise's most controversial characters. Introduced early in the novel version of The Fellowship of the Ring, Tom is a seemingly ancient and mysterious being who nevertheless proves to be friendly enough to the Hobbits when they encounter him. Originating from early poems by J.R.R. Tolkien, Tom saves Frodo, Sam, Merry, and Pippin from the dangerous Ent known as Old Man Willow. The Hobbits spend two nights with Tom and his wife, Goldberry, during which time it's noted that the One Ring seems to have no effect on Tom -- a rarity, given the corrupting influence the One Ring possesses. He even ensures the four make it safely to the Prancing Pony, where they meet Aragorn and continue their journey.
Although he's referenced again later in the original novels, Tom never plays a major role in the story -- and has been subsequently cut from almost every major adaptation of The Lord of the Rings trilogy. The character remains popular with some book readers, who argue he's a fun and mysterious addition to Middle-earth's grand scope of characters. Others argue that his exclusion from adaptations makes perfect sense, as he's, at best, a minor figure in the story and, at worst, a distraction from the main plot. Peter Jackson agrees with the general sentiment of the latter camp, as Tom does not appear in his adaptation of the trilogy. However, if the above Lord of the Rings theory is true, Tom was hiding in plain sight as the Witch-king.
The Witch-king plays a major role in the films, wounding Frodo at Weathertop in The Fellowship of the Ring and leading the assault against Gondor in The Return of the King -- ultimately setting up his final fate, falling during a battle to Éowyn. If Tom and the Witch-king were indeed one and the same, then Tom was actually in more films than one would have expected for the character, even in the best of times, and one of Tolkien's most mysterious figures might have his deep well of power explained by a dark reinvention.
The Lord of the Rings films are available to stream on Max.