I don't think there are very many. I break movies down into just a few categories: Drama, Comedy, Horror, Action and Documentary. I've never been a huge fan of diving deep into sub-genres. Never once have I described a film as a Dram-Com-Doc or a Hor-Com-Dram.
I especially don't approve of Thriller and Suspense as major genres, as I barely accept them as sub-genres of Horror. They're just words for people who don't want to admit they like being scared or because they think the word Horror implies a lesser quality film.
Don't get me wrong. There are clearly other genres that are hard to place beneath those Big Five. Sci-Fi, Western, Fantasy and likely a few others. The only reason I wouldn't include them off the bat is 1: My penchant for keeping things simple and 2: The use of the word 'main' in the question. Yes, to some, Romantic Comedies and Westerns are main genres. To me, they are not. They are speciality genres. You'll notice that the Big Five I've put forward are vague, and cover a lot of ground. What Western isn't an Action movie or a Drama or both?
To Stephen King, every good story is a Horror story. To me, every good movie is a Drama. When you don't know what to call something, it's a Drama. Even many successful comedies have great dramatic moments. If I had to pick one term for all creative endeavors, it would be Drama. It reflects what storytelling is all about: getting people involved, making them care about characters and watching their varied, arcing journeys to resolution.
Short Answer: I could easily be convinced to extend the Big Five to a Big Ten, but I'll never accept the really sub-genre-y shit like Zom-Com, Disaster Films, Road Movies and so on. Those things describe what you're going to see more accurately, but that doesn't make them an entire genre. To me, if you go beyond ten genres, you're opening yourself up to nearly a hundred. No joke.
Note: The Martian is not a Comedy.