Actually, contrary to popular believe, there's no law in Singapore that one must carry his/her identity card in public. But of course, carrying it makes life easier, for both the member of public and the police. In a so-called spotcheck, what the police looks for is suspucious (e.g.loitering) or undesirable (e.g. rowdiness) behaviour. The police first and foremost wants to verify the identity of the person being checked.
If you're checked while not carrying your identity card with you, you can still give your particulars verbally to the police. However, the police shall then have the discretion of believing or disbelieving you. If you're not convincing enough, or if the circumstances that you're in isn't accounted for satisfactorily, the police may detain you in station to verify your identity. Note that this doesn't amount to an arrest, at least not yet.
After the question of identity, the next things the police looks for are personal belongings, e.g. any contraband items, or even weapons etc.
The other common type of spotcheck is the roadblock, usually to look for speeding, drunk driving, driving without licence etc. traffic offences. It also checks for taxi passengers for potentially wanted fugitives. Roadblocks are usually (but necessarily) conducted between 1 a.m. and 4 a.m., as these are the most common hours for drunk drivers and wanted fugitives to move around town. And also, it causes minimal disruption to working hours traffic. However, roadblocks can also be conducted in daytime if, say, there's a robbery getaway car on the run.
Anyway, as another forummer has pointed out earlier, Singapore police is relatively tame compared to many other countries. E.g. in the US, it's common that the checking officer whips out his revolver and point at you first before talking. But in the US, even the public understand and accept that the police has to assume that all suspects are likely to be armed, given the high rate of firearms ownership, both legal and illegal. In Malaysia and Thailand, roadblocks are usually conducted with M16s pointing at your car.