The three novels of the Lord of the Rings all describe a War between Good and Evil. But the title of the first book – The Fellowship of the Ring – doesn’t say anything about grand battles or last stands (even though there are plenty of those things in all three books).
Instead, Tolkien chooses to emphasize something we all want: fellowship, which also means friendship, companionship, and kindness. So while The Fellowship of the Ring may be a novel about war, it’s definitely not pro-war. Tolkien emphasizes friendship as the only way for the side of Good to fight against the Evil that Sauron brings.
And then there’s the Ring: Sauron’s Ring, the One Ring to Rule Them All. This Ring is what’s known in super-special film circles as "the MacGuffin." What is a MacGuffin, you ask? It’s a term director Alfred Hitchcock came up with to describe the central object that makes the plot of a movie or book move forward. The Horcruxes in Harry Potter, the Hammer in Thor, the Holy Grail in Indiana Jones and the Last Crusade – they’re all MacGuffins. They all provide a reason for the plot to happen the way it does.
The point of the Ring as a MacGuffin is that the Ring is absolutely necessary to make the quest of Lord of the Rings work as a story. At the same time, the Ring does not have to be a Ring – it could be any powerful token of Sauron’s might. The novel would work just as well if it were a sword or a stone or a hamburger or an iPod. Consider: The Fellowship of the Rubber Chicken.
Tolkien probably picked a Ring instead of a rubber chicken because there are lots of magic rings in Germanic mythology (his specialty). Rings are also neatly portable – It would be tough for Frodo to go on his epic walking tour of Middle-earth if Sauron had stuffed all of his power into a mountain or a large tree. The point is, the Ring is the whole reason the Lord of the Rings trilogy exists, so it seems only right that the Ring should make it into the title of the first book.