It's not only in the U.S. that cap and trade (CAT) is a controversial approach to try to lower greenhouse gas emissions. A report written in Australia, and critical of CAT, has sparked a battle over censorship. Finally the report's author and the leading science agency in Australia have reached a compromise that will allow publication there.
Currently there are CAT schemes in place in the European Union and among the northeastern states in the U.S. Here's the website for RGGI which administers CAT across ten states in the northeastern section of the U.S.
Japan's current government is looking at introducting CAT in the next two years. Some major metro areas of China have long had carbon trading schmes in place. But there is no national emissions regulation or CAT in China.