Hi! I haven't been yet in Dubai but I heard many things of it. There are many sightseeing options listed here: http://www.dubaicityguide.com/mobile/sight_seeing/sight_seeing.asp. Beside this you can go to see Burj Al Arab Hotel Dubai, a seven star hotel, the only one of its kind in the whole world, and also go shopping! And if you do so, don't forget that bargaining is a must...start negotiating at half price the vendor asks :)
Another thing I would surely try out is indoor snow skiing at the Mall of Emirates. - (2007-12-18)