The only person we know who was expelled from Hogwarts was Hagrid and his transgression was quite big:
He allegedly did open the Chamber of Secrets
Harry was threatened several times to be expelled but it never came to that, even when he broke the rules for not doing magic during summer vacation time.
So - what does it take to get expelled?
Background of the question:
Actually being expelled from Hogwarts is quite the disaster for a wizard/witch. The ability to use magic is comparable to the ability to read/write for Muggles - a very core skill that is needed for practically any profession in the magical world.
A Muggle who is expelled from school could just join another school and finish his/her education. Expulsion from Hogwarts results in your wand being broken and you are forbidden to do magic for the rest of your life.