The national religion of Dubai is Islam. Hence, most of the Dubai culture has been derived from the Islam. Nevertheless the city of Dubai is quite tolerant. People from different cultures have found place in Dubai.
However, being exposed to cross culture has not resulted in the loss of Dubai culture and heritage. Whether it is in terms food and clothes or festivals and art, you will find the rich culture has been retained.
The people in Dubai have big families and young people generally have arranged marriages. In Dubai a great deal of respect is given to the women. They have now begun participating in the corporate world as well.
You will find the art and craft of the Dubai noteworthy. You can get hand fans called "mehaffa" and pots called "birnah" and "hibb" that have a cooling effect on their contents.
You can see constructive features called "barjeel" that work like air-conditioners by bringing in cool breeze. Heritage villages have been built to preserve such works of art and craft.
However, the culture here is not rigid. You will notice the incorporation of modern elements like modern pop songs, Hollywood and Bollywood movies, pubs and nightclubs, foreign food, etc.
You will notice that the people of Dubai wear long, loose dresses called "dishdashah". The men cover their heads with a cap called "thagiyah" covered by a piece of cloth called "gutra".
Women sometimes cover their faces too with a "burqa". If you are from another cultures you are allowed to wear what you desire, within the limits of decency.
Ramadan is the most important festival celebrated in Dubai. During this time the people in Dubai observe fasts, which start at dawn and end at dusk.
You will notice that during this period people from other background and culture are also supposed to adhere to Dubai culture by fasting like the natives. This period is followed by the celebration of Eid Al-Fitr.
The other popular festival is Eid Al-Adha. Here you can celebrate these and occasions like marriages with great pomp and gaiety. "Liwa" and "ayyalah" are two traditional dances of Dubai culture.