Well, in Japan you can get just about any battery type you can think of at the larger camera/electrical stores. Prices for common batteries like AAs or AAAs are quite cheap, they are commonly sold in packs of 10 or 20.
Lithium 'button' batteries are also commonly available, but more expensive (starting at around US$3-4)
Hong Kong has lots, similar availability to Singapore. Don't know about price though, haven't been there for about 4 years.
Most other countries in Asia have the common AA, AAA, C, D, 9V types, and some of the more common button types like CR2032.
Graham