My 6 yr old son has a set from IKEA that was acquired when he was 3. The quality is terrible, but husband has bolted it together. If we ever move, a chainsaw will be required and it will be no more. The only reason we have it is because it is shorter than normal ones. The top bunk comes about to my chest (I'm 5'4").
He's never had any issues with the bed. However, my 3yr old daughter (who, frankly is just stubborn and accident-prone), has fallen off of it twice (no major injuries), despite rules and restrictions. She's just not allowed to go up there and every time she goes in his room I say, again, "don't get on the top bunk because you've fallen off." Some things just take repetition, although, once this bed dies, no one will be getting another bunk.