Singapore has many interesting Souvenirs.
Most tourists love Merlion which is bizarre half-lion,half-mermaid mascot. You can easily find Merlion keychains,t-shirts or fridge-magnets in Chinatown or in Mustafa Centre .
You must have used tiger balm for your aches and pains and this ointment is very popular in many countries. Why don't you take some as gifts for friends who might need them?
Kaya is sweet bread spread made of coconut,milk,eggs and Pandan leaves and is typically eaten slathered on toasted bread in traditional breakfasts. You can buy them in all supermarkets and even in the airport shops.
These are quite unique and may contain picture of Singapore's landmarks or orchids. There are even plates with iconic recipes such as chicken rice or chili crab.Places where you can find such decorative plates are "SuperMama" at2 65 Beach Rd, Singapore 199544 and "The Farm Store " at 261 Waterloo Street #04-20, 180261.
You can find different varieties of chopsticks in Chinatown which you can keep for yourself or give as gifts.