Beer in Asia can be divided into three general categories: imported beer, brand-name local beer, and local favourites. Imported beer is usually expensive, to the point where you are spending a lot more money to drink the same brews you can get at home. Imported beer is usually available at most western-style bars. It can be hard to find microbrews like Sam Adams, Saranac and Anchor Steam. However, along with American beers like Budweiser, brews from larger European companies such as Guinness, Bass, and sometimes Boddingtons are usually available. Occasionally they can also be found in convenience stores. Once in a while you may even find a nice ale, but usually most imported beers are big name lagers; Carlsberg, Becks, Bud, MGD, and all the other international names. Big name Canadian lagers such as Labatt's and Molson aren't very common. The Philippines' San Miguel is popular in various Asian countries.
Expensive Branded Beer
Brands including Sapporo in Japan, Tsingtao (Qingdao) beer in mainland China, and, to an extent, Singha beer in Thailand, are expensive. Price is no guarantee of quality. While you may want to try these local branded beers, it's sort of like going to Australia and drinking Foster's ie, it's a sure-fire way of letting the locals know you are a visitor. Fosters is promoted worldwide for the international market. While not a part of Asia, do try the local microbrews in Australia and New Zealand - they're fantastic.
The beer most locals drink in Asia is lager, often supplied in 600ml (about a quart) bottles. The taste for lager has evolved from the time Germany introduced beer-brewing to parts of China. Most famously this occurred when the Germans colonised the Qingdao province in the early part of the 20th Century. Occasionally, the local beer is a malt beer, an example being Singha beer in Thailand.
Local beers are usually quite drinkable. Anything lacking in taste is well-compensated for by price. In China, you can usually buy a bottle of the local brew for about 2-3 Kuai (US$0.25). In Taiwan, 600ml of Taiwan beer costs a bit over US$11.
Local beers vary a great deal in mainland China with some cities having their own brews. Beijing has Beijing Beer (Beijing Pijiu) or Yanjing Beer (Yanjing Pijiu). Beers usually vary by province. To figure out the popular local brew, just watch what the locals pitch back on the streets at the BBQ vendors. A word of warning, the locals often like their beer warm.
In Thailand, the local beers are Chang and Singha. Chang is the local favourite, even though it's made by a foreign company (Carlsberg). It's cheap, usually costing about US$1.50 in bars for that big 600ml beast.
In Bali, Indonesia, the two big local beers are Bali Hai and Bintang. The locals seem to prefer an alcoholic concoction called 'Arak' over beer.
You'd never go to Asia to eat hamburgers, so why go there and drink Bud? Eat local, drink local.