The crime rate in Cyprus isn't especially high, and there's no reason for travellers to take anything beyond ordinary precautions. While muggings and violent crime are extremely rare (especially once away from Lefkosia), it's always a good idea to be vigilant with personal property. Secure valuables whenever possible, avoid keeping all essentials in the one place, and lock vehicles, leaving belongings out of sight. Be conscious that crowded tourist areas and public transport are the most likely sites for pickpocketing and other property crime.
It pays to be extra-cautious in the area surrounding the Attila (or Green) Line that demarcates North and South Cyprus. While the barbed wire and sentry posts are usually good clues to keep clear, these are less visible in parts of the east. If you do want to cross the Line, make sure you do it in a designated area and in a lawful fashion.