Science Fiction, Adventure, Fantasy
First and foremost, Star Wars is science fiction...or, more specifically, space opera, which is an epic and more fantastical form of science fiction.
Sci-fi purists would argue that the genre needs to be...well, not realistic, but plausible. For a good example, look at the spaceships in 2001: A Space Odyssey, which were based on actual NASA vessels with just a little speculation thrown in.
Star Wars is dedicated to a practical universe—that is, a universe where everything looks like it has a practical purpose and has been used in practical ways—but with Jedi mind tricks and hyperspace-breaching weapons on display, they don't see a need to stick close to reality. Coupled with the larger-than-life figures and do-or-die heroics on display, it makes space opera a slightly more comfortable fit than pure sci-fi.
That also helps out its other big genre a lot. Nothing says "adventure" more than hopping in a spaceship and seeing what's on the next planet, and Star Wars has always been part of that tradition. Last-minute rescues, impregnable fortresses, alien races with weird customs and mating rituals that will sear themselves into your nightmares? We see those in old-school stories like Tarzan and 20,000 Leagues Under the Sea. Star Wars just adds a high-tech sheen to it all.
Finally, you can't talk about Star Wars without talking about fantasy: ancient worlds full of monsters and magic where some young lad or lassie leaves their humble farm and learns valuable bits of wisdom on the road to defeating a great evil. Like every other film in the series, The Force Awakens actively embraces its inner Tolkien, and underneath those spaceships and lightsabers are the old-fashioned horses and swords that epic fantasy heroes are very familiar with.