If I had to say which reminds me about the LotR, it would be also few ones from Led Zeppelin, but not Battle of Evermore (although it fits in there and it surprised me when I first heard it some time later). Btw I really don't think BoE refers just to Middle-Earth: apart from mentioning the Ringwraith, there is no distinct mention of anything else of Tolkien, and I think it's more or less "general" - about fantasy, or fairytales, and so on. There is also one song from a band I actually don't know, they are not my kind of music, but I noticed that in one of their songs - otherwise they don't have anything in common with Tolkien or even fantasy at large - they sing about a man who returns home drunk or something like that, don't know the text, just there is a word about his wife, that she "cried like hurt Nazgul".
I'm actually surprised no one has mentioned the Blind Guardian (or maybe I overlooked it?). Their album "Nightfall in Middle-Earth", which is all about Silmarillion, and sole songs like "Lord of the Rings" I don't find actually drawing me to the world of Tolkien, but they talk about it nonetheless, so I'm surprised they were not even mentioned (especially, if there were Nightwish mentioned, who are very similar kind of music, but do not sing about LotR explicitely, and the BG do - at least in these few songs).
But back to the original question, songs which remind ME of ME (ahem... you know what I mean
) are some from Clannad, but as well Led Zeppelin's Stairway to Heaven (as someone has already mentioned) and Black Dog (don't ask me why; I just used to have them on tape - ah, the ancient times - together, and it reminds me somehow of the other Wizards than Gandalf. Yeah, when I listen to it, I imagine Radagast, Saruman, and the Blue Wizards. But don't ask me why, really don't know). There are also songs where the feeling is more common, like Pink Floyd's "Breathe". And yeah, I could add some songs from the Beatles remind me of Frodo and Sam's journey to Mordor: namely "With A Little Help From My Friends", "A Day in the Life", "Magical Mystery Tour" and "Strawberry Fields Forever"