Realism, Dystopian Literature, Tragedy
We can definitely state with no ambiguity that All Quiet on the Western Front is not comedy, children's Lit, or a fairy tale. It's also not postmodern, experimental, or a romance.
But it could be just about anything else. Some things to consider:
One could argue that it is a coming-of-age story, but, if so, then it's equivalent to a story about a baby being suckled by porcupines. Paul comes of age but then—poof—he dies. Usually coming-of-age stories result in the main character learning a lesson, which he then takes to heart and passes along. This is like a coming-of-death story, or something analogous.
And it certainly could be labeled a tragedy. There isn't anything not tragic in the book. A daisy doesn't even grow in the end.
But at a higher level, All Quiet on the Western Front might best be labeled realism or dystopian literature – the battlegrounds are as close to those of 1984's mind-numbers as anything else. This is the complete opposite of utopia. What makes this story so powerful is that the story was, for all intents and purposes, real.