Valencia is one of the safest cities in Spain. However, as in any other metropolis, don't yawn and follow some simple guidelines. Firstly, street thievery is rampant in Valencia - try not to show where your wallet is hidden or how much money is in it (ideally, pay everywhere with a credit card).
Valuables and passports are best left in a safe in a hotel. Keep your bags in sight, don't hang them on the backs of chairs in cafes or place them on the floor. Carry your backpack on your stomach in crowds, belt bags over your shoulder.
Another local "color" is crowds of gypsies who "work" in groups. If you're alone, never try to talk to them - at best you'll lose your wallet.
The second problem of Valencia is scammers, who are found even among cab drivers. For example, all cabs here are equipped with meters, and if it suddenly "breaks down", just take another car.
Thirdly, never leave things in a parked car. Moreover, even at a traffic light a bag lying on the seat can be stolen by local "skillful" people. They often act with an accomplice: one of them honks the horn, informing you that you have a "problem" with your car, and while you find out what's wrong, the accomplices pull things out of your car.
And finally, the golden rule of all tourists: in the dark, do not go alone in remote parts of the city, especially in the neighborhoods behind the beach Malvarossa and Cabañal (gypsy villages).