As long as you stay in the TUCSON city limits you should be fine. Do not go to South Tucson which is a city of its own. It is a working class area with gangs and lots of car theft reports. To be on the safe side, just stay north of downtown. Its definitely not one of the most dangerous cities around, but like every other large city, there can be some fairly dangerous parts.
Every city has its share of crime. Tucson is no exception. We have a high amount of property crimes such as vandalism, burglaries, auto thefts and thefts from vehicles.
I worked on patrol in Tucson for 9 years. I have answered a lot of calls at the hotels situated along the I-10 corridor. They tempt travelers because of their low rates and proximity to the interstate. For these same reasons, they also attract thieves, drug dealers, prostitutes and others we wouldn't want to meet up with in a dark alley or a dimly lit street. That isn't to say that you can't stay in these hotels. You will just have to take precautions for your safety and the safety of your belongings.
I have seen a lot of questions posted on the board about the safety of certain hotels and certain ares. The Tucson Police Department has a great tool on their website, which will allow you to put in an address and see what kind of crimes are associated with it.
Crime is an issue in the city. During the daytime, you should have little or no problems with anyone. When the sun goes down, that is another story. Pretty much all of Tucson except for the way north part of town has shootings. In my neighborhood in Central Tucson, I have heard and see about 20 shootings in the area in the past year. The South side of town is the worst. Drugs, and bad stuff all over that part. Just use caution and you should be okay.
In 2004 and 2005, Tucson had the higest property crime rate in the country. Don't be scared, just be careful.
It is important to be at least aware of this, and to note that you need to always lock your car, hide valuables from sight inside your car, and be very careful with where you park your car. Also beware of car thefts, which are also very common. Do not leave your car running unless you are inside it.
If you're biking, you must always lock your bike, even when leaving for just a couple of minutes. If you stay here long enough and ride a bike, it will be stolen. There's just no getting around it.
Violent crimes in Tucson are nothing to get excited about, though. Car-jackings are relatively rare, as are muggings, assaults, murders, rapes and most other things to get really worried about.
Whenever you are going to do any crazy things in Tucson... do not break any law. It seems that they have a lot of police on streets (at least in a downtown and on 4th N. Avenue) you to feel safe and comfortable.
Enlarge my picture to see what strange vehicle the Tucson police use (on the left).