As Singapore is only 1.5 degrees north of Ecuador, the weather is usually sunny with no distinct seasons. Rain falls almost daily throughout the year, usually, sudden downpours rarely last more than an hour. However, most rainfall occurs during the northeast monsoon (November to January), occasionally with long periods of continuous rain. Spectacular thunderstorms can occur throughout the year, at any time during the day, so it's a good idea to carry an umbrella at all times, both as a sun shade or rain cover.
Between May and October, forest fires in neighboring Sumatra can also cause dense haze, although this is unpredictable and comes and goes rapidly: check the site of the National Environment Agency for current data.