We have a trampoline in our yard - we got it about 7 years ago. The first Summer the kids were on it alot. We made rules that only one kid was allowed on at a time. No one under age 6 was allowed at all. Our nieghborhood boy was the most amazingly agile kid I've ever seen and could flip forward backwards and sideways - really. My kids are not that nimble.
It is considered dangerous. We haven't been able to change homeowners insurance since we got it since it's grandfathered on our old policy and all new ones have exclusions. My son came home from our neighbors across the street with a concussion one evening when he and the other boy hit heads. It was scary. We already had the trampoline but probably wouldn't have gotten it had it happened before.
A note regarding the trampoline "parks"... We took our youth group a few months ago - the big difference is that the parks have staff who stop kids from doing certain maneuvers & limit the number of people on any one trampoline. Plus the trampolines go up the walls so there's no possibility to tip off onto the ground. Much of the bounce area is for basketball or dodgeball and the kids are really very closely controlled - or at least they were at the park we went to.
I think there are alot of things that carry the potential for injury - skateboards and skateboard parks (my friend's 19 yr old son died in a freak long board accident when he hit a rock, the board went out under his feet and the back of his head hit the ground), bicycling (I broke my collarbone when I was 20 when a car ran a stop sign), tree climbing, backyard pools (my SIL fell from a slide and fractured a vertabrae when she was a teenager), etc.
So - yes - they're dangerous. I think they get a worse rap than bicycles and skateboards because homeowners get sued over accidents related to trampolines where as no one gets sued regarding bike & skateboard accidents so they don't have to be excluded. For whatever it's worth our trampoline hasn't been touched in about a year - seems the only time anyone is on it these days is when we have a family party - the little kids are on it. it was expensive, we hoped it would be a way our kids would get some physical exercist - but it's ended up being like the treadmill inour spare bedroom - used initially but sitting there now - unused... At least there's no clothes hanging on it!