Autodrome Dubai - tear around a race track in someone else's car. Allow 2-4 hours.

Balloon Flight - expensive way to see sand dunes. Allow a morning.

Desert Safari - many companies offer tours, allow most of a day.

Helicopter - allow an hour. Quick, efficient, expensive way to see Dubai.

Parachute Jump / Skydiving - visit Umm Al Quwain airfield and fall out of a plane. Allow half a day at least.

Ski Dubai - great for beginners, ok for intermediates. Experts will get bored quickly but it's worth a trip for something different if you go with a mate. Allow 3-4 hours.

Wild Wadi - water park, allow 3-6 hours.

Dubai is a fast growing city with a rapidly increasing number of attractions for tourists. On this page are several guides and plans for tourists (or residents) to help them enjoy their time in Dubai. A few general sightseeing tips, followed by suggested itineraries for 1-3 days or a week in Dubai.

The Big Bus tour is a good way to see Dubai and get oriented. The explanations are reasonably helpful and they're not trying to peddle favorite merchants for carpet buying etc.
There is a discount coupon book called The Entertainer UAE available in supermarkets and bookshops in Dubai for about 175 dhs. Included in the 2007 edition are a couple of buy-one-get-one-free Big Bus tour tickets which will save you 150 dhs if two adults are travelling - almost covering the cost of the book. Make sure you get the general Entertainer book, not the specialised ones. Other coupons include restaurants, fast food joints, Ski Dubai and Wild Wadi passes.

As a general rule, use the mornings to do any visits to Deira and near the creek on Bur Dubai side. Traffic (vehicle and pedestrian) gets much busier in the afternoon/evenings.
Shops are open till 10pm or so every day. Other commercial activities stop on Fridays. Government departments are closed on Fridays and Saturdays.

Dubai is relatively safe and crime free compared to most cities but be alert as you would be anywhere. Lock your car if it's unattended. Mind your bags and pockets in crowded areas. If an area looks dodgy late at night, it probably is. Naif Square in Deira is a good example if you're looking for that sort of thing.