One of the more familiar non-Chinese cuisine would be Indian Cuisine. In some non-vegetarian Indian outlets, you can also find roti prata served with vegetarian curries. If you are vegan do ask if the prata and curry contain ghee, egg or dairy. Indian cuisines, especially North Indian ones, uses dairy products in many of their dishes. South Indian cuisine is more vegan friendly, some of the dishes include Dosa (Dosa batter spread thinly on a skillet and fried and eaten with curry) and Putu mayam (a sweet dish of rice noodles served with brown sugar and grated coconut). Malay cuisine is less veg friendly, but many of the malay cakes, we call them kueh (koo-eh), are vegan friendly. Singapore also has a place which serves Mediterranean vegetarian cuisine. Called Original Sin it is located at Holland Village. This high end restaurant is vegan friendly. My friends told me that the dishes at Yogi Hub are special, so do give it a try if you come to Singapore for a visit.
Indinine cafe at Suntec City is also a good try for special dishes. All these places are vegan friendly. Hawker centres can be a great haunt for vegetarians, I shall give more details next time.