I do honestly believe Tolkien didn't intend to make Sam and Frodo's relationship romantic. But I also know from experience that characters start doing their own thing after you've been writing them a while, and I'm sorry, Professor, but those two hobbits REALLY seem like a couple. And they seem like they have been for YEARS before this quest. Or, at the very least, Sam's in love with Frodo, and Frodo complacently humors it. I'm not even trying to be a swoony shipper here--the conditions of the quest are not exactly sexy--nor am I trying to be subversive. This is my (admittedly 21st-century) writer's instinct talking.
Sam does marry Rosie after they get home, so maybe the strain of the quest is what finally ends the relationship. I can see how the Ring would do that. (Curse you, Ring!) But up till then--really, I'm trying to bring non-shipper-ish, clear-headed analysis to this, and they STILL feel like a couple to me. I keep shrugging off one eyebrow-raising endearment only to have them voicing new ones the next page.
Yes, LOTR is a book full of close male relationships--which it would have to be, given the absence of females. But none of the other guys act the way Frodo and Sam do. Merry and Pippin are close and chummy, but theirs is more a bromance. Legolas and Gimli make a nice Odd Couple or pair of Grumpy Old Men willing to travel together after the quest, but that's about all. And Legolas does say how he, and others, will follow Aragorn anywhere because they love him so much, but that feels like a kingly-worship thing, along with an Elvish-courtliness thing.
None of them sleep in each other's laps the way Sam and Frodo do. They don't gaze at their buddy as he sleeps, find him "beautiful," and murmur, "I love him" (Sam, The Two Towers). They don't fondle each other's hands and say, "My dear" (both Frodo and Sam, lots of times). When parted from one another, they don't long only for that fellow, "for one sight of his face or one touch of his hand." (Sam looking for Frodo, The Return of the King.) In fact, only Éowyn so far, to Aragorn, has used stronger words of romantic love, and shown stronger signs thereof, than Sam and Frodo have to each other over and over throughout.
Sam is Frodo's servant, which does alter the nature of how they'd relate to each other, especially since this is a fantasy world where social norms could be different. Frodo's role as "master" could--people say--account for Sam's brand of loving devotion. Tolkien claimed he meant their friendship to resemble that of an officer and his batman in WWI. A rural gentleman and his familiar valet, perhaps, one could also say. As regards the cooking and pack-carrying and looking-after that Sam does for Frodo, sure, I accept that. But I'm sorry, Professor, my instincts say he's gone beyond the feelings of a faithful servant. Or else being a batman apparently means acting like someone's boyfriend.