Singapore is a popular stop for students backpacking through Asia. It isn't, however, as reasonably priced as its neighboring countries. Expect to pay a minimum of S$30 a night for a bed in a very basic guest house.
You may notice "student" rates for ferries, for example -- this only refers to people ages 12 to 18. Carry your international student ID with you at all times, though, as entertainment venues may offer discounts.