As far as I know, Mewtwo was still the main pokemon in Cerulean Cave, same as the US/Europe versions. It was possible to get Mew in all versions from a glitch (search YouTube for videos).
They gave Mew away at various events across the world - real life events like at the Toys R Us store. There may have been more events in Japan since pokemon is even more popular there.
There was also a Mew event recently for HG/SS on wi-fi in Japan. No word on whether it will come to the US/Europe yet.
EDIT: Mew event running from October 15-30 2010!