Pretty much everything!
Alcohol - although the UAE is a Muslim country, purchasing and drinking alcohol in a licensed club, bar, or restaurant is legal for non-Muslims who are over 21. To buy alcohol for home consumption one must have a personal liquor license, which can only be obtained once the person has residency status, which can take 4-8 weeks. The cost is approximately 105 Dh (approximately $30US). (Obviously, while drinking is permitted as described, being drunk and/or disorderly in public is not permitted!)
Clothing - "regular" clothing, and high-end designer clothing and sportswear is easy to find.
Bathing Suits - these are easier to find in the UAE than in Saudi Arabia, but you will want to bring at least one with you.
Electronics - electronic stores abound, selling the latest in computers, audio, and video equipment. Videos and DVDs are also available, but these may have been censored.
Jewellery - jewellery shopping in the gold souqs is very popular for expatriates (and locals) and rarely does an expat leave without a sizable gold collection.
English-Language Books - English reading material can be found at book stores and grocery stores.