Unlike other cities all over the world, Dubai is one of the safest cities in the world; the crime rate is relatively low as the punishment to those who do unlawful things can be severe.
There have been crimes in Dubai but it is very low, some of the crimes that have been in Dubai are usually burglaries, there have also been home burglaries in Dubai in the month of July and August because lots of foreign homeowners leave the City to go home to their own country. Some burglaries happen at jewelry stores and such.
It is still essential to maintain personal safety when travelling to another country, it is your own responsibility to keep your passport and visa documents in order and make multiple copies in case of theft. If someone should take your documents from you or you might have lost them somewhere you can always go to your embassy in Dubai and ask for guidance in what to do.
It is not advisable to go anywhere with a stranger, you can ask for a tourist guide in your chosen hotel or a travel agency can provide you a tourist guide wile you are in Dubai.
Everyone who is traveling to Dubai has to respect the customs in Dubai, Dubai public bars and nightclubs do not serve alcoholic drinks, you can buy at duty free stores when arriving the UAE Airport.
When you are traveling during Ramadan you are not allowed to eat or drink in daytime, this is why it is best to avoid traveling to Dubai in the month of Ramadan.
Safety Regarding food and drink
Water is safe to drink in Dubai but it is recommend that you buy mineral water which you can ask for in your hotel, in restaurants and other public facilities.
Food is also perfectly safe, as Dubai is very hygienic.