I'm lucky to have never had braces (although a dentist would argue I could use some for my bottom teeth, but it's not an issue for me), so I've never accidentally cut the inside of my mouth on them.
But I have bitten off some several chunks of tongue when I've been in fights before, or have fallen down.
My own fault really, in tense moments and when pumped on adrenaline, I automatically push my tongue into the back of my teeth. I have no control over it, it's just an automatic response. But it has meant my tongue has been caught between chompers before.
On a similar note, if you want to vomit quickly (without stuffing fingers down your throat), apply a sizable dosage of table salt to that area under the tongue. Works pretty well.