As far as places go, Singapore maintains good order and has minimal crime rate. Violence rarely erupts in the somewhat conservative city. The occasional handbag / wallet /mobile phone may go missing if left unattended but things are usually peaceful.
Travelers may very well run into more problems with authorities than criminals. Not that the Singapore government is out to get you, avoid things such as:
- Spitting, littering in public
- Jaywalking
- Talking to airport staff about bombs, terrorists, threats and other security
- Having firearms or replicas of firearms, especially in the airport, as even an empty cartridge or lone bullet by can still be considered as firearms
- Public demonstrations without a permit – if you ever find yourself in one, you are recommended to put some ground between you and the crowd
In general, doing the opposite of what signs say is a bad idea. Just remember to keep your valuables close to you.
Other issues may include strong public displays of affection, and laws to do with “outrage of modesty”.
Try to keep private activities private. Even though some days can be particularly hot, please do not lose your shirt in any public areas except beaches. There are laws that make male to male sex illegal but a president address on the matter suggests that it won’t be heavily enforced.
Touching others when and where it is not appreciated can trigger the “outrage of modesty” law so make sure you have the other person’s consent before anything happens!