Singapore is a very safe country with low crime rates. Pickpockets are not unknown but, in general, crime is not a problem. This is not surprising given the harsh penalties meted out to offenders and the fact that hundreds of suspected criminals are held in jail without trial simply because the government does not have enough evidence to convict them. The importation of drugs carries the death penalty, which is regularly carried out. Simply, drugs in Singapore should be avoided at all costs.
The nanny state of Singapore takes a tough line on antisocial issues - the most famous being its ban on chewing gum (well, it does mess up the pavement and could stop the MRT from working). While having gum for your own consumption is no big deal, bringing it in bulk into Singapore will attract a heavy fine - the standard way of stamping out un-Singaporean activities.
Smoking in all public places, littering, jay walking and eating or drinking on the MRT are all punishable with hefty fines.