Sounds like out of the pages of Dr. Seuss, but my double trouble loved the Wubble Bubble, which looks like a bubble but plays like a ball.
I first got to see the Wubble Bubble up-close at Element Associates Social Suite at Blogger Bash. Since my duo are crazy about bubbles and balls and are always trying to steal my yoga ball, I knew this would be a great toy for them. Heck, my own mind was blown (no pun intended).
The Wubble Bubble is approved for play indoors and outdoors, but we've only tried it out inside so far. It takes 2 minutes to inflate to 3 feet tall, however, since my boys are still young we only inflated it to about a foot and a half. Here's a helpful video on how to inflate it, which we also watched beforehand. You can also deflate the Wubble, which is great for storage too.
The Wubble Bubble is made from super-thermo-stretch-tacular stuff, not as durable as a yoga ball, but much lighter, thus allowing my boys to catch it, kick it, squeeze it and make it fly. My boys put it through the test too and all are fine. What's also cool about the ball is that it's bounces are unpredictable as sometimes it bounces backwards or to the sides, thus keeping my boys running in all directions. it also makes a fun bouncing sound when you hit it, which is appealing and fun for kids. As a result, my boys spent a good amount of time just drumming on it.
The Wubble ball is available for only $19.99 at Target stores nationwide and that includes the battery-operated air pump, but after that it's even cheaper when you want another Wubble Bubble and already have a pump.
Disclosure: I received a sample Wubble for review purposes, but because I'm a human and not a robot, all opinions are my own ;)