I have had a trampoline for years, and I have thrown some pretty crazy things on them like double flips with late spins and whatever.
But I have never been hurt on one. Why? Because trampolines teach you how to crash and like the other guys said 'be aware'.
You learn safety, if you try absolutely stupid things that are way above your level then yes you can get hurt. if you just take everything one step at a time, and work your way up then you will not get hurt.
There is a way to crash/fall. Trampolines help give you the coordination, timing, air sense, and control that you need to develop this.
Some parents don't get trampolines for their kids because they don't want them to get hurt. Which is understandable, but in reality not having things like this makes you uncordinated and can end up getting hurt more - on stupid things.
I know this kid who has very protective parents, they will not let him try anything crazy or jump on trampoleans, so he doesn't do anything crazy.
I do some pretty crazy things sometimes, but this kid has gotten hurt more than I have.
Why? He has no coordination skills whatsoever. He's broken bones by tripping on the ground. Or he'll try skateboarding once, fall off and break more bones.
If he had a trampolean he could've learned how to fall correctly - to minimize injury.. - to roll out of things.
Eat. Sleep. Breathe. Ski.