daria, it all depends on what you're doing at the moment that caused the ring to break.
i've only broken one ring, but wow, was that a STOOPID moment that caused it...
it wasn't annealed yet (my big mandrels are too long for my kiln so i batch anneal), but i liked it so much i decided to wear it anyway. i was at my cousin's, playing with his youngest daughter, i think she was 3 or so at the time... and she said she'd teach me a new game. we sat on the floor, and she said- "it goes like this-" and started pounding on the floor with both her hands... she was so funny doing it, that i joined her, completely forgetting that i was wearing an un-annealed glass ring!!!
and that's how i learned that when you pound an un-annealed ring to the floor- oh well, it breaks!
anyway, i think i was lucky not to hurt myself, but breaking the ring this way, it couldn't have broken away from my hand, only into it. i guess i was lucky it was a thin band (oh, it was so comfortable too...
)