Singapore has a well deserved reputation as a safe place to visit. Crimes against tourists are relatively rare, but you'll still want to watch your valuables in crowded places, such as the Orchard Road, Raffles City or Bugis Junction shopping areas.
Singapore has so far escaped the kind of terrorism that has threatened Westerners in many other countries in the region. As a result, there are few precautions at hotels and shopping centers around the island. Cars and people are allowed free access to such places without any searches. This is not to say that you should be at all concerned about your safety in Singapore. On the contrary, you can and should enjoy your stay in Singapore without concern for your safety.