Singapore is one of the cleanest, best organized and safest countries in the world. You could be fined heftily for any minor wrong doing, such as jaywalking, spitting and eating or drinking in trains and buses.
If you are caught littering, a Corrective Work Order might be imposed on you, so it is not surprising that fines get rougher for more serious crimes. Corrective Work Order is a punishment in Singapore (introduced in 1992) for the offence of littering which requires the offender to spend a specified number of hours picking up litter in a public place
Don't even think about drugs in Singapore, as death penalty in for possession of relatively small quantities of drugs is strictly enforced in Singapore (this is made known to all the travellers through a prominent note on Singapore immigration card, which all visitors have to fill in before entering the country).
Chewing gum is not a drug, but it is (almost) banned in Singapore as well. Click on the video link below to get a somehow provocative insight into this controversial Singaporean ban.
Nevertheless, don't let the stories about Singapore being a terrible place where you can be fined any time, anywhere and for anything scrap it off your travel itinerary. As long as you follow common sense and read the signs, you'll be fine in Singapore.