Jetstar, is a budget airline that flies regularly to Singapore from Thailand, Indonesia, Philippines, Vietnam, Taipei, Hong Kong. Their airplanes are a bit small but their prices are definitely cheap. Tiger Airways is another budget airline which flies to Singapore from India, Australia, China, Philippines, Indonesia, Macau, Malaysia, Thailand, and Vietnam, like Jetstar, their airplanes are also small. If you're in the Philippines, a local airline, Cebu Pacific, also flies to Singapore daily and their local prices sometimes beat that of Jetstar and Tiger Airways if you happen to book within their promo period. If you don't mind paying a little premium, Singapore Airlines also have flights from major Southeast Asian cities but like I've mentioned, their prices have a bit of a premium. 

To get the cheapest flight possible, its best that you sign up for newsletters with these budget airlines so you can be alerted of any promos they have which would slash your airfare to around half of their regular price.