Dubai is a very safe destination and the emirate's crime rate is very low, largely due to the harsh penalties applied.
As a tourist, you can feel safer than at home. There are no particular areas to avoid, even at night.
Think about safety - anyway
Nevertheless, as always when travelling, you should of course lock up valuables and make sure you have control of your belongings. A camera or wallet left too carelessly can be stolen - even in Dubai.
An amusing detail in this context is that the Dubai police have an impressive fleet of police cars in the form of luxury brands such as Ferrari, Lamborghini, Aston Martin, Bentley and Mercedes SLS. Several of the sports police cars are driven by female officers.
Not the time to try to outrun the police in Dubai, then.
(Page updated 2015-08-27.)