The Thai tuk tuk is known as the "auto rickshaw" in India (sometimes shortened to "auto") and the "bajaj" in Indonesia (from the most popular manufacturer, Bajaj Motors). All three share essentially the same design with the driver up front, the passengers behind, and the two rear wheels driven by a bicycle-chain system.
As our Indian host put it, "When accidents happen, there's no arguing, because usually one of the drivers ends up dead."
The Philippine variant, the tricycle (or traysikel) is a little different; it is essentially an unmodified motorcycle fitted with a sidecar, and a roof over both. Two passengers sit in the sidecar, beside the driver, and one sits side-saddle behind.
I also believe Malaysia has the tuk tuk, although I've never been there to confirm it (or to find out what it's called.) China, Taiwan, Singapore or Hong Kong, apparently do not.
blaaf says: I can confirm that Taiwan does not have the tuk tuk; taxis are everywhere in cities. Can't say for China, but kunming at least has taxis, no tuk tuks.