We have constant jumping over here -- up to six little boys under six at a time playing here (2 are mine) and a very active 10 yr old girl and her friends.
The best jumping toy we've found for age 1-5 is the Rody horse
http://www.rodytoy.com/
VERY sturdy. The youngest ones just sit on it and bounce, and as they get older they can hold the ears and hop across a room with it. It is great to have two if you have lots of kids playing together. THe kids also play with the Rodys imaginatively, stabling them, "feeding" them, etc.
We also love the hop balls for older children, mostly on the back lawn but also in the playroom if we clear the floor:
http://www.hippityhopball.com/
We have the largest size, which dh and I can also use. They are not so good for younger children as one needs pretty good coordination for these.
We use salvaged couch cushions with covers I've sewn for them -- don't know if this would help the dust mite issue. They came from a very springy couch.
We also have a giant beanbag chair that zips out into a king-sized flat foam mattress, the king-sized chair fand footstool from this company:
http://bagthebed.com/
It was pricey and takes up a lot of room in our playroom, but is totally worth it. Children jump off our playroom couch or a low stool onto the chair (with our cushions surrounding it on the floor, and supervision, always, to ensure one-at-a-time and no toddlers trying to jump from the chair to the stool, like my youngest tried to do once).
You can kind of flatten it like a pancake, which makes it lower to the floor or you can fluff it up and it becomes a great big marshmallow of a thing that kids love to jump on and sink into, depending on age/safety needs. We also enjoy sitting on it, lol!
I often set up a course -- jump from stool onto beanbag chair, hop off onto couch cushion on floor, climb slide and go down it, crawl through play tunnel, back to line up at stool to jump on chair again.
Sometimes we unzip the whole mattress and make a great big jumping area.
We used to have a couple of play couches in the playroom and our "jumping place" was set up by pulling the cushions and our spares off the couches and making a couch-cushion mat between them. The children would jump on the low couch frames (springy) and off onto the floor cushions.
A friend used a kingsized mattress on the floor between two couches with foam mats lining the wall between the couches. It was the best jumpy place, ever.
I had one of those inflatables. It lasted me less than 2 months before ripping unrepairably at the seams. Not a good investment for my crew, unfortunately, but fun while it lasted. Also had an excercise trampoline for a while, but it didn't last well either. I'm considering one of those with the handle, my dd's playschool had one like that that was big enough for 2.
The key for me is NEVER EVER EVER to let the toddler and preschool-aged little ones jump ANYWHERE without parental supervision. By the time the reach the age of my 10 yr old dd, they know enough about safety rules that supervision can become intermittant. I'm one of the moms who doesn't let her kids go on full-size trampolines, which are big in my neighborhood, btw. I really believe that jumping is important though, so I suck it up and supervise, and put a lot of time and money into fun alternatives...
And we do go to playgrounds , outdoor and indoor, a lot. And drop-in at a gymnastics club.
I agree with the poster who said that if you make it a point to give the children jumping time, it really takes the edge off their need to do it when and where they shouldn't.
But we let them jump on the beds, too- just too tempting with a queen and single pushed together in one giant bed.
