LOTR is really one book in 3 volumes so it would be hard to read it out of order the first time. I reordered my reading of v.2-3 to follow the story straight on one side of the river, then the other.

Some other series are written so that the stories stand alone, others don't. With some SF writers, it's more like they create a world and set lots of stories in it so each is pretty independent of the others.