Frodo and Sam: ho or no?
The somewhat ambiguous nature of Sam and Frodo's relationship has long been a topic of discussion among scholars and fans alike. Most people agree that the bond between them is very close, whether they consider it platonic or not; the two spend most of the story in each other's company, share many thoughtful conversations, trust each other with their lives, and end up living together even after Sam's marriage. Sam also sleeps with Frodo's head in his lap several times during their journey, kisses his hand or cheek on numerous occasions, and feels torn between his master and his wife.
Interestingly enough, Sam is the only one of the five prominently featured hobbits to show any attraction towards a female during the course of the novel. Frodo and Bilbo are never in any openly romantic relationships whatsoever; Merry and Pippin get hitched later in life to two hobbits we know nothing about. Sam's love for Rosie, rather than being subtext, is plainly obvious to himself and to everyone around him, to the point where even Rosie's father has caught on. He thinks about Rosie wistfully as his strength wanes on the slopes of Mount Doom, and later blushes mightily when Frodo talks about how brave and famous he is in front of her. Eventually she bears him a grand total of thirteen children, and only after her death does he leave Middle-earth to see Frodo.
Nevertheless, many have commented that the term "friendship" isn't quite strong enough to describe Sam and Frodo's bond. Some have called it brotherly; others speculate that Sam is a polyamorous bisexual, or believe that Frodo is Sam-sexual, or ship Sam/Frodo/Rosie. An example of a purely platonic relationship is that of Frodo and Merry or Pippin, who are described as Frodo's "closest friends" in FOTR, ch. 2. Note that this quote is from before the Quest kicks off. Frodo has undoubtedly been fond of Sam for some time, as shown at the end of this chapter, but at this point Sam is still his slightly dim-witted gardener. Later, as the journey grows more arduous and the two of them are forced to go on alone, the already unusual master-servant relationship (Frodo is never shown giving Sam orders, and calls him a friend, which implies equal status) will shift into something more, well, ambiguous as the two of them become more dependent on each other alone.
Although any Ho Yay was certainly unintentional on Tolkien's part - being a devout Catholic writing in the 40s and 50s, he would most likely have disapproved of queer relationships - there are two relevant quotes from the books that liken their relationship both to a marriage and to an animal partnership. One appears in The Two Towers, during the passage where Sam battles Shelob to save Frodo. There Sam is described as "a small creature [...] that stands above its fallen mate."
The second is written in the epilogue (published posthumously), where Sam tells his daughter that Celeborn and his wife, Galadriel, were separated when she sailed west. Elanor responds by likening Sam and Frodo's relationship to theirs, noting that Frodo also left Sam behind when he departed for Valinor. She tells Sam, "He knew that [...] Galadriel would leave him. I think it was very sad for him. And for you, dear Sam-dad." Sam does not correct her comments as a childish misunderstanding. Neither does he explain to Elanor that he is in fact married to Rose Cotton, or that the two relationships are of a different nature; instead he says that his sadness has lessened and confides that he hopes to see Frodo again, thereby implicitly validating his daughter's insights.
Finally, it must be mentioned that neither Rose nor any of her family appear in Fellowship at all, which renders Sam's first thoughts of her and her brothers in the middle of R.o.t.K.note as a Remember the New Guy? moment. It is likely that Tolkien was aware of the fumble he had committed at the end of The Two Towers (the first quote above) and created Rosie to counteract it. It should also be noted that Tolkien is sometimes considered to have fumbled with Eowyn in regards to Aragorn, but the remedy for that case involved a character first mentioned in Fellowship and having a significant role in Frodo & Sam's half of Towers. The movies, to their credit, set up Rose by including a moment between her and Sam at Bilbo's party.note
The Lord of the Rings is no allegory of any kind, but rather fanfiction of a sort inspired by Norse and (more broadly) Germanic mythology, as well as various other sources (chief among them being Celtic Mythology, Classical Mythology, Greek philosophy, and The Bible—i.e. the greatest sources and deepest roots of Western culture as a whole). There are too many references to ignore: The One Ring is from Nibelungenlied and Plato's Ring of Gyges; Gandalf is Merlin and Odin who were powerful sorcerers and made sacrifices to be reborn; when the elves travel across the ocean they go to Tír na nÓg *ahem* Valinor, which lies to the west and to which you can only go with the elves. And of course, Eru Ilúvatar is (explicitly) YHWH the Creator, the Valar and Maiar are angels, Morgoth is Satan, and Elves are Man before the Fall.
The nature of evil in Middle-earth
Ownership is the root of evil in Middle-Earth. Melkor's fall was not based on his desire to create life, but his desire to control the life he created. Compare his experience with that of Aule, who also sought to create life, but since he did it without selfish intent, he was forgiven and his creations, the Dwarves, were give true life of their own. Evil intent is defined by the attempt to bend life to your own individual will.
Note that both Sauron and Saruman were originally servants of Aule before they turned to evil. They were both craftsmen, skilled at making things. The temptation to enslave others, to take a creature with a will of its own and bend it into a mere thing to be controlled, is particularly strong in those who are builders. Aule himself is able to resist this temptation, because as a pure Artist he takes joy in the act of creation, and has no desire to impose his will over anything or anyone. It's not evil to create, even to create life. But it is evil to assume that once you create something, it belongs to you forever.
Tropes in LOTR
The majority of tropes used in The Lord of the Rings are well-explained, unlike in the majority of its imitators. For instance, Mordor has large fertile areas offstage where food is grown, thus explaining how Sauron's armies survive in the volcanic hellscape around Barad-dûr. The Ring is also more than just a convenient MacGuffin — its effects matter too much for that. This is largely due to the immensely elaborated Back Story and Tolkien's life-defining experiences in The Great War.
There were, though, some tropes J. R. R. Tolkien couldn't justify to his satisfaction, not helped by the fact that he updated his mythos constantly over a period of decades, creating a minor Continuity Snarl at times but never quite reaching the Shrug of God. He spent years trying to decide how orcs could be Always Chaotic Evil without being born evil or soulless — since Eru would not give creatures inherently evil souls, on moral grounds, Morgoth was unable to create souls, and Tolkien believed anything without a soul would be a mere animal — but he never found any answer he liked. It was philosophical niggles like this that stopped him from publishing The Silmarillion in his lifetime. His son Christopher did it posthumously, to the delight of all Tolkien scholars, and most of his readers.