Star Wars: The Old Republic were able to start logging into the game simultaneously across the world... assuming "the world" meant North America and Europe. The Pacific regions were unfortunately deferred to a later launch date, something that provoked some ire from fans in that area. However, the wait is now over for an official launch day. A launch of March 1st has been announced for Singapore, Australia, New Zealand, and Hong Kong.
Naturally, there are fans in those regions who would prefer to play on regional servers but have already started play on existing servers via imported copies of the game. BioWare is promising that players in these regions will be able to transfer characters for free for a limited time following the launch date, allowing everyone to move to regional servers if desired. The game is also available for pre-order now, so if you're in the affected region and want a copy, best take a look at stores near you for order options.