There have been various other posts with the same question, but the main things are:
Dubai Creek - take an abra
Burj Khalifa - tallest building in the world, but pre book your tickets if you wish to go up in it
Burj Al Arab - glitzy 7* hotel - has to be seen just the once!
Shopping - Mall of the Emirates, Dubai Mall, the gold and diamond souks etc
Water parks such as Wild Wadi or Aquadventure at Atlantis Hotel
Rugby 7's if you are here at the right time
Outside of Dubai
Dune driving - with/without traditional shisha and belly dancing at the end
F1 in Abu Dhabi if you are here in November
Al Ain - Jebel Hafeet mountain is amazing
Drive over to Oman
Dolphin watching in Musandam
It would help if you said what you are interested in, the age range, how long you are going to be here for etc etc.
Camels almost 8 years ago
Dubai is famous for their Friday buffet brunch! I know that sounds a bit odd as an attraction, but these brunches have about 10 different rooms filled with food from sashimi to pizza bars. The prices is all inclusive and you can stay all day if you want to.
Here is a pretty good list of the best: http://www.timeoutdubai.com/restaurants/features/2432-the-citys-best-brunches about 7 years ago
There is alot to experience in Dubai, below are a few:
Take a water taxi ride on a beautiful day in Dubai
Enjoy awesome view of skyscrapers along the Sheikh Zayed Road from the water. The Water Taxi is a great addition to Dubai's amazing infrastructure & a great way to get around the city.
Fascinating Space Age Architecture
Buildings shown in the above photo are:
One Business Bay - wedge shaped with increasing floor area as the building rises.
Prism Tower - looks like a prism with a helipad on top.
Iris Bay - oval shaped construction looks like a crescent moon.
Mall of the Emirates (MOE) in Dubai
MOE contains approximately 2.4 million square feet of shops.
It is not the largest mall in Dubai, but really the brand behind Dubai's shopping allure.
Mall of the Emirates features 520 international brands, including department, fashion, lifestyle, sports, electronics and home furnishing stores and the largest Carrefour in the city.
Burj Khalifa and Downtown Dubai
Absolutely STUNNING view of Burj Khalifa & Downtown Dubai!
Downtown Dubai, Emaar's flagship project in Dubai. At the centre of the community lies the tallest building in the world, Burj Khalifa, an architectural and engineering masterpiece, offering premium residential, office and retail space and houses the world's foremost luxury Armani Hotel.
The Dynamic Tower - Da Vinci Tower
AMAZING!!! Changing landscape without having to leave the comforts of one's home.
Architect David Fisher has designed a 200-apartment 420-metre (1,378 ft) moving skyscraper in Dubai where each of the 80 floors rotates individually, taking in the views of the city in a one-hour orbit.
This building is currently under constrction. about 7 years ago