We have one and the kids LOVE it. We've had it for two years and they never get tired of it. I could extole the virtues of exercize, balance, coordination, etc. It's as wonderful as you remember from childhood.
No one has had any serious injuries yet, but I'm waiting for it. I'm not too protective that way and I don't want to be. Kids get hurt. What's the worst than can happen with safety nets? My son actually did bounce off of it when the net was unzipped once, and that stopped my heart but he was fine. Sure someone could break a bone, but that can happen on monkey bars, too... oh wait, I don't see monkey bars any more. Frankly I think that's a loss and I don't want to raise kids who are afraid of trying fun things. Who hasn't broken a bone?
My dd has had stitches in her head twice, once from falling out of bed at a hotel while asleep, and the other when she slipped in socks on hard wood and hit her head on a chair. But we still let her sleep in beds and wear socks. She does know, however, that the next time she needs stitches, mom will do the stitching or she'll have to get a job.
With that said, there are legitimate concerns about friends playing on the tramp. Good luck keeping them out. We forbid friends from going in the treehouse already and we'd have a hard time forbidding the trampoline, too. It's probably a lawsuit waiting to happen.
Your homeowner's insurance has to be notified and your rates will go up. Make sure your yard has a fence, too, or else you're just tempting neighborhood kids to go for a jump. You can get sued for that, too. (What the heck is wrong with us and the lawsuits?)
OH, and in the state of Texas you actually cannot adopt a child or foster a child if you own a trampoline. Statistically they are risky.
We still have one. I'm not taking it down.