Singapore is one giant sauna at any time of the year. November to January are the wettest months, but the other months are not exactly dry either. From March to September there is a distinct lack of refreshing winds. Generally, expect temperatures to average around 31°C (88°F) during the day and linger around 24°C (75°F) at night.
Go anytime. Climate is not a major consideration, as Singapore gets fairly steady annual rainfall. Instead, coordinate your visit with one of the various festivals and events: Thaipusam is a spectacular Hindu festival, occurring around February. If shopping and eating are major concerns, April brings the Singapore Food Festival and the Great Singapore Sale is held in June.