It's nice to have free Wifi and Internet terminals in most Asian Airports.
The wifi works for sure in Changi Airport. But if you are not a local, you need to register.
If not, use one of these modern looking terminals around the airport.
I think Hong Kong's airport is the best. The moment you touch down and waiting for the long queue to clear immigration, you get signal! All you need to do is click OK to their terms and conditions and you are connected, no registration required!