Violence against individuals is rare and tourists aren’t specific targets. Nevertheless, avoid Muslim Quarter backstreets, and be cautious walking around the Old City at night (when almost everything is closed anyway). The important weekly Muslim prayers around midday Friday sometimes get passionate if there’s a hot Palestinian-Israeli issue in the news. Emotions can spill into the streets of the Muslim Quarter as the crowds leave the al-Aqsa Mosque.
As in any major tourist destination, pickpockets can be a problem: keep purses closed and close to you, and wallets in less accessible pockets. Don't leave valuables in parked cars, and use hotel safes.