Of course most of the time it is legal, you do have the right to snap people on the street.
There are of course exceptions, e.g. sensitive installations where no photography whether of people or the surroundings are not allowed.
That said, there is law of street, if the Big Muscular Man punches you because you are shooting his Quite Pretty Girlfriend non-stop (which quite some "street photographers" seem to indulge in) and following them around, I guess you can't really blame him. Of course the law doesn't allow for his punching of you, but what for invite trouble? Practise due-discretion.
And don't shoot from awkwards angles, otherwise you might risk others misunderstanding your intentions. Its ok to shoot on the streets but exercise courtesy and respect for others and I think you'll be fine
don't shoot upwards on staircases and escalators. people might think you're gunning for *ahem* shots especially if there are pretty (and not pretty) girls in skirts (short and very short) standing above.
This has been discussed before, in great depth, so you might want to a search. My input would be to note that public places/private property often get confused. Shopping centres, office buildings etc are private property, and the limits of the property sometimes extend beyond the structure itself -- there have been too many stories of photographers demanding their "rights" to shoot in public areas that are really private pty. These idiots don't necessarily get into trouble themselves, but spoil things for the rest of us.
Shooting strangers per se is not illegal in Singapore, but if it's for commercial use, clients may want a model release (esp if they are marketing overseas).
Other than that, there are some places (with the red signboards saying Protected Place) that you might want to steer clear of. And since 9/11, transport infrastructure e.g. SMRT stations, have become touchy subjects too.