I had absolutely no idea how dangerous trampolines were until several years ago through work I was involved in a trampoline injury case and did research on trampoline injuries. After that, I would never in a million years buy one, and I cringe to think of my daughter ever getting on one.
If you get a trampoline, please never let more than one child at a time on it and institute a no flip rule. If those rules are broken- take it down or get rid of it. The net may prevent falls off the tramp, but it won't prevent injuries. Most serious injuries on trampolines are not caused by falling off the tramp, but by how you come down on the mat. Most parents have no idea how dangerous trampolines are. You can come down on the mat wrong and have all kinds of injuries including breaking your neck and being paralyzed and in a wheelchair the rest of your life (that's usually from trying to do a flip and landing on the mat on your head instead of on your feet). You don't even have to be doing anything wild to get horribly hurt. In our case, the kid was just jumping straight up and down, but another kid was on the tramp at the same time also jumping straight up and down. That is a major danger as if more than one person is on a tramp the tension of the mat will be wrong when people come down. If the mat is taut when you hit it, you can do serious damage. It's kind of like jumping off a roof and hitting the solid ground. The kid in our case broke his leg at the growth plate and his legs will likely never be the same length. There is case after case out there of kids breaking bones just because they came down wrong, or at the wrong time, when they weren't doing anything wild or unusual. Almost every trampoline you see will either have a booklet or a tag on it warning that only one person should be on it at a time, and that is to avoid liability for these type injuries. Also be prepared as some homeowner's insurance companies will cancel your insurance policy if they find out you have a trampoline. There are many cases where parents have sued other parents or neighbors for not properly supervising their visiting children after their kids were injured on a trampoline.
I would not have thought twice about letting my daughter get on a trampoline before that case. We won't ever have a trampoline and I really hope my daughter is never on one (although I know she probably will be at some point, but if I ever see her on it at the same time as another person, I can't even tell you how much trouble she will be in).