Elements of the underworld and of heroic katabasis crop up all over the place in fantasy literature. Sometimes, the underworld is literally the land of the dead, as in Greek myth (like that depicted in Maggie Furey's Artefacts of Power series, which I haven't read in years and must re-read...), sometimes it is just a similar sitation that is reminiscent of the ancient underworld (as in Harry Potter and the Half-Blood Prince).
The Lord of the Rings doesn't include a great deal of obviously classical mythology; Tolkien was more inspired by ancient Norse and Germanic myths, and he disapproved of mixing and matching mythologies in the way that C. S. Lewis did. However, the appearance of the Paths of the Dead in The Return of the King is pretty clearly influenced by ancient katabasis.
Strictly speaking, the journey to the Paths of the Dead is not a katabasis in the sense that it is not specifically a journey to the land of the dead. There are a couple of different afterlives in Tolkien's mythology, with one for men (and, presumably, hobbits, dwarves and so on) and a separate one for Elves (I'm not sure what happened to Orcs. I haven't read The Silmarillion or all of the Unfinished Tales, so maybe someone who has can enlighten me!). The Paths of the Dead don't go through any of them; rather, they go under a mountain where a group of oath-breaking military ghosts have been cursed to remain until they fulfil the oath they broke. Like the Harry Potter example, this is reminiscent of katabasis, as the characters have to go underground and walk through a place filled with dead people, rather than a literal katabasis. The dead are also somewhat more lively than the classical variety, though perhaps even more unpleasant.
I have to confess, although normally I'm a sucker for an underworld story and am particularly interested in epic descriptions of the underworld, the Paths of the Dead has always been one of my least favourite bits of The Lord of the Rings. In the book (which I first read aged about 10 or 11) I was never quite sure what was going on - Aragorn had joined up with his old buddies and wandered off somewhere, Gimli didn't like it, then we don't hear from them again for ages. By the time they finally turn up again I just want to get back to Frodo.
The film had the potential to do something pretty cool with this section, and I am generally in favour of having the dead show up at the Battle of the Pelannor Fields, since it makes it clear how useful they are, though I think perhaps they shouldn't have won quite so easily - maybe have a slightly smaller army of dead people so it takes longer. My biggest problem with them, though, is that they're green. Why are they green?! It's not an army of the dead, it's an army of Borg. Or maybe they're all related to Slimer from Ghostbusters. Anyway, they look weird.
Why, why are they green?!
I suppose part of the problem is that there's so much going on by this point, one thing is always going to seem less interesting than the others. I love the story between Merry and Theoden in the book, and Eowyn is my hero(ine) so I guess anything that takes me away from that story is bound to seem less interesting. I think I also prefer actual katabasis - that is, a journey to the place where we go when we die - to these similar journeys, which have some of the same elements, but don't offer that privileged glimpse into the next life that real katabasis does.
On the other hand, the disadvantage of a classical journey to the land of the dead is that most of them (with some exceptions) are utterly miserable. The dead are empty and shapeless. If they can talk, they say how much they envy the living, or they continue to mourn wrongs done to them while alive, or the cause of their death. The whole place is dark and shadowy, and although descriptions of Tartarus are sometimes included, we rarely see any sign of the Elysian Fields or the Isles of the Blest (though follow the link for a rare exception from a work of satire). Only in comedy is there any hope for a decent afterlife; all of which is rather depressing for all concerned. A scene like the Paths of the Dead allows the author to indulge in some properly gloomy, scary, spooky underworld imagery without suggesting that this is what all the characters have to look forward to when they eventually die, and this may be its greatest achievement.