The 2K Forums have news that the activation restrictions have been removed from BioShock, including the limitation on the number of allowed installations (thanks GamesRadar). Word is:

Good news! As promised, all activation restrictions, including install limits, have been removed from BioShock PC as of today. You don’t have to patch or install anything for this to go into effect for your copy of BioShock – it’s already done!

Enjoy your time in Rapture, and thank you for supporting BioShock and the 2K teams.