The UAE is a multicultural society so a big range of clothing can be seen from western to bright African gowns and Indian style outfits. Even in nightclubs, clothing can be seen as expected anywhere else and expatriate women are allowed to wear bikinis on the beach. Almost anything can be worn, however the UAE is a Muslim country in its core so local traditions should be respected. The place, event, location (such as which Emirate), and the people that may be around should be considered. It is advisable to carry a scarf to cover exposed shoulders in case one is confronted with an awkward encounter.
Heat is a big issue so fabrics should be light but not transparent. However, there is air conditioning everywhere which can make closed areas such as malls particularly cold.
Although especially in Dubai women are seen in short skirts and tank tops, it is advisable to observe local standards of modesty. Men should avoid wearing shorts in public places and women should try to not wear revealing or transparent clothes that expose the shoulders, legs and cleavage. A good rule is if the sleeves are short, the trousers or skirt should be long and vice versa. Abu Dhabi is a little more conservative than Dubai and more care should be taken when visiting the Northern Emirates.