The massive Empty Quarter dunes present an awesome driving challenge. If you're in the country during the cooler months and you like adventure, rent a four wheel drive, find a group of eager drivers (you'll need at least three vehicles; never drive alone in the desert) and set out for the sand. Be sure that your vehicle is insured for off-road use and that you have the proper equipment. If you've never driven off road, you should first learn the ropes with one of the several tour companies in Abu Dhabi.
Camping
A trip to the desert isn't complete without a night under the stars. You can arrange camping adventures with a tour company or rent a four wheel drive and buy the equipment yourself. Camping supplies are surprisingly cheap in the emirates and there is no need to buy high quality equipment. In fact, you could probably buy a tent and two sleeping bags from a hypermarket for less than a guided tour. Never go out in the desert alone!