Thailand does not require registration, but authorities prevent travelers from re-entering shortly after their stay (cracking down on "visa runs") which has caught some tourists/nomads off guard. The strictest punishment is banishment for a maximum of 10 (IIRC) years.
Like China, Japan requires registration with the local city office if you are staying with a long-term visa. Although it should be noted that China applies this to all visa types whereas Japan allows tourists to stay without registration. Failing to register with the local Japanese city office can result in banishment.
As with registration in China, you are not told this information upon entry of these countries. If you blindly travel you will be caught out (and usually punished). However, asking around and doing the research before you travel can prevent that from happening.