You cannot spit, chew gum, or litter in Singapore (not that you should do the first and last anywhere). You also cannot drink in public, and there are designated smoking areas throughout the city, so do not walk and puff.
Eating and drinking on trains, forgetting your seatbelt, and using your mobile phone while driving are all punishable no-nos as well – in addition to good old jaywalking, speeding, and running a red light. If you must go into a healthcare setting for some reason, you are still required to wear a mask.