Don't use your left hand for greeting, gesturing, giving something to, or eating with a Malay, Indonesian, or Indian person—it's the hand traditionally used for toiletry purposes. Refrain from kissing or touching the opposite sex, as some communities might be offended. Note that it's common for men, particularly from the Indian subcontinent, to hold hands or interact affectionately.
If you're invited for dinner by Chinese friends or business acquaintances, leave some food on your plate to indicate that your host's generosity is so great, you can't eat another bite. At a formal meal, rice will often be served among the final dishes rather than at the same time as the meat and vegetable dishes. Don't pile your plate full of rice at the end of the meal. Your hosts may think that they didn't provide you with enough food. There's no shame in asking for a knife and fork instead of chopsticks. Hindus are often vegetarian, Muslims don't eat pork and must abide by strict food preparation guidelines, and some Chinese may be devout Buddhist vegetarians. Check on dietary preferences before dining with multicultural company in Singapore.
It's mandatory that you remove your shoes in places of worship. You should cover up your arms and legs in Indian temples and Muslim mosques. For women, a head covering is advisable. Use extreme caution when visiting mosques, perhaps seeking the permission of locals or the nearest person in authority to enter, and then asking where you may walk and what you may do. There may be areas where you aren't permitted to go, particularly if you're a woman.
Don't litter: it's against the law and you can be fined S$1,000. Chewing gum stuck in train doors was blamed for the shutdown of the subway system more than ten years ago, and as a result the government banned it from being sold in Singapore. You may bring it in for personal use, but be sure to dispose of it properly.
Smoking is not permitted in public service vehicles or in most buildings. You can be fined up to S$1,000 for smoking in prohibited areas. Most restaurants and some bars have outdoor terrace areas where you can light up.
Don't publicly criticize Singapore, its politics, or its leaders, and refrain from jokes about them unless you're sure of your company—Singaporeans can joke all they want, but you're an outsider and a guest. Share your opinions only when asked and, if negative, in a gentle manner.