Etiquette
The majority of Singaporeans don't wear shoes inside their homes, thus it's polite to take them off before entering someone else's home if you've been invited. However, socks are fine as long as they are not overly dirty. Additionally, many houses of worship demand that visitors take off their shoes before entering.
Be ready for a lot of pushing on the MRT during rush hour (even just to get off), and everyone scurrying for the last available seat in a fairly orderly fashion. Despite notices requesting a little more courtesy, this is common. Simply follow the flow.
When bringing gifts, be mindful of taboos. Avoid white flowers and any products (food or otherwise) involving animals as they may offend people (usually reserved for funerals). Clocks and knives are both symbolic of ending relationships and passing away, and some Chinese people have superstitions about the number four.
It should be noted that opening a present in front of the person who gave it to you is deemed impolite. Instead, wait until they've departed before opening it. Hindus and many Muslims in Singapore abstain from alcohol consumption.