It wasn't that long ago that there was almost no crime here at all, but then the influx of labor from outside the country did the trick. That said, the OAE in general, and Dubai in particular, remains one of the safest and most comfortable places on the planet.
Just keep your belongings to yourself if you don't want to fall victim to pickpockets, and don't walk around working-class neighborhoods at night - that's all the precautions you need to take.
And it would not be out of place to remind ladies that in a strict Muslim country, it is strongly discouraged to expose your legs and shoulders outside the tourist area.
