I'll second the comment on H.O. insurance and the very real possibility of a neighbor kid gettting hurt and his or her parents suing. Having said that, I think they're great, BUT . . .
I screwed around on a neighbor's tramp as a kid without getting unlucky. Later, in my seriously skiing addicted days, I was into freestyle skiing (primarily mogul skiing) and during my last two years at the Univ. of Nevada at Reno, I augmented the ski team ski conditioning classes with trampoline classes. Don't recall the coach's name, but he had been an NCAA trampoline competitor who had broken his back in competition, which ended his competitive career, but the guy was REALLY good. We all first learned about fundamentals, how to avoid getting hurt, and how to train to take on more difficult tricks. To get to anything more advanced than back drops, knee drops, etc., we had to demonstrate that we could competently perform all those moves first. Having been through those classes and having my eyes opened, I'd highly recommend finding a coach to start them properly and teach your kids the basics, which are the building blocks for recovery and safe landings when you get out of shape in the air (like being under-rotated in a flip).
And then I'd make sure that you set rules about your kids and others who use the trampoline. (That'd probably include getting a form for assumption of the risk, indemnity and hold harmless signed by parents whose kids know about and will give permission to their kids to use the tramp.)
Having said all that, I'd love to have one -- absolutely GREAT exercise and a lot of fun.
