Among Singapore's entry requirements for visiting foreigners (accessed here) is:
Onward or return ticket (if applicable)
When is this requirement not applicable?
Yes. In my experience they do. Or at least the airline which will get you there will require you to have an exit ticket in order to board.
I was traveling from Phuket to Singapore without an exit ticket from Singapore (although I had an exit ticket from Sydney 2 weeks after) and the airline wouldn't let me board without an exit ticket. It was a pain. In the end I ended buying a $40 ticket at the airport which I never used.
I know this answer lacks any specific information regarding actual regulations, I am just sharing my experience. Hope it helps.
EDIT: When I answered this question the title was "Does Singapore require all tourists to present proof of onward travel?"