I recently saw this list of photos of cases of hyperdontia which is when you end up with more teeth than you might have bargained for otherwise. This strikes a chord because I had this. As a child, I underwent a series of at least two (that I can recall) operations to have an extra 5-6 teeth removed. And though the first, epicly distrubing photo of a tooth-filled palate is apparently photoshoped (according to this dentist who provides some context to the whole thing), this is nevertheless something that does happen.
In my case, I did have a couple of teeth growing out of my palate - I used to like scratching my tongue on one - and a few that grew out sideways out of my gums. One time, when they put me under, they forgot to take out all the ones they were supposed to, so as soon as I came out, they put me under a second time - which in hindsight, was probably a bit much sedation-wise for a six year old.