I've gotten through Singapore without either an entry or exit stamp (or even the passport being opened!) but that's not the norm.
On the way in we got delayed on the airplane (lost item? It's been long enough I've forgotten) and by the time we got to passport control they were talking to each other. They saw US passports and just waved us on through.
On the way out the idiot taxi took us to the cable car station instead of the train station. When we hit passport control at the train station (just in front of the train itself) the train started rolling. We (and several others) were waved on through--we got on that train 70 seconds after it started moving.