There will always be crime in any major city, but there seems to be less crime around the Tempe campus than the metropolitan Phoenix area. The ASU police are directly across the street from the University, and they are constantly seen patrolling the area. Students feel really safe walking around at night, and it definitely helps that ASU has a service to take you back to your dorms in case you do not feel comfortable walking around in the wee hours of the morning. Most of the crime on campus is petty theft (like the infamous bike thieves or campus break-ins where people will steal equipment), potential sexual assault, and of course drug- or alcohol-related issues. You will find the occasional bar fight that breaks out on Mill Avenue, but overall the campus is a safe zone. Nevertheless, every individual should stay aware and not take things for granted because anything could happen at any moment, not just at ASU.
As far as personal health goes, vaccinations and other preventative practices are advertised around campus by the Student Health Center during flu season and periods when more sickness breaks out on campus. The health center also provides guidance in sexual health and safety by giving students the information and protection they need to practice safe sex. So long as you keep your head straight and use common sense, your safety in all aspects should not be an issue while attending ASU.