Ernest Hemingway is a major contributor to Modernism, a genre literally born from the tragic events of World One. It was impossible to process the millions of casualties and the scope of the war’s destruction. Hemingway and other Modernists are known as "The Lost Generation," (see the "Overview" for more) in part because they were lost in a world blown to pieces by the war. They sought to make something new out of some of those pieces, to find something new which could help the world to heal. For Hemingway, that something new was his storytelling style, which we talk about, coincidentally, in "Style," and which we can see in A Farewell to Arms.
This probably goes without saying, but the novel is a War Drama, because it directly shows us the war. It’s also Historical Fiction since it recounts historic events. As you might have guessed, mortality rates are high in this novel, and the devastating fate of one main character means we’re definitely in Tragedy-land. The treatment of bad weather as a portentous mood-setter is a good indication of Gothic literature (again, the death, death, and more death is a flashing sign, too). But what makes the Tragedy all the more tragic, and the Horror all the more horrific? The intensity of the Romance, that’s what. The love story between Catherine and Frederic is unforgettable, as is Frederic’s love for the men he works with. Finally, the exquisite craft and the depth of the characters found in the novel, and the fact that intellectual types don’t mind being seen reading it, means we can also call it Literary Fiction. And we’re done.