Action, Science Fiction, Heist
It's kinda hard to miss all the action going on. Every single level, from reality to Limbo, has shooting involved, and sometimes lots of it.
There's also lots of car combat and chasing shenanigans in the first dream level, anti-gravity hand to hand combat in Level #2, and even people having gunfights on skis (as if gunfights needed to be any more dangerous) in Level #3.
Every movie has a foundational genre, a basic type of entertainment that we can expect when going to see it. Inception is an action movie, through and through.
We know that as soon as you hear "science fiction" you're getting out your light sabers and Vulcan salutes, but just because Inception isn't that kind of sci-fi doesn't mean it isn't sci-fi at all.
Let's start with the basics: dream sharing. Inception takes place in a world where the military has invented a dream-sharing device that not only puts people to sleep in a dream but also somehow connects their subconsciouses so they can experience the exact same dream space. Not only that, but they can build the dream space themselves by picturing a very specific location.
Even the dreams are highly structured things: if you die in the dream or fall in the real world you wake up, you can feel pain, and there is an exact connection between dream time and real time.
Inception is definitely science fiction… even though Cobb never dreams of Tatooine or Tralfamadore.
Last, but not least, this bad boy is a heist film. At first, Nolan had planned on going full heist, doing the whole explanation-as-it's-all-happening-Ocean's-11-style thing.
However, he realized that a film about dreams needed to be an emotionally charged film and that heist movies are, by and large, too glamorous and superficial (which is why they're awesome). Still, there are undoubtedly heist elements left over from the initial concept: the assembling of a team of trained people, each with a specific function, a montage of strategizing, and the actual carrying out of the plan which requires stealth, deception, and guns.
Just like any good heist.