When Bioshock was released, 2K Games was criticized for using SecuROM copy protection system and restrictive activation policy which allowed only two simultaneous installs of the game on different PCs.
"We have in the works a revoke tool which you will be able to run on your machine if you want to free up that key and move it to another computer", 2k responded back then.
2k games finally released the Bioshock Activation Revoke Tool and you can get it from the downloads tab.
Excerpts From Revoke Tool FAQ :
Q: What is the BioShock Revoke Tool?
A: The BioShock Revoke Tool will de-activate the current license on the computer contact the activation server to free up the activation, for future use.
Q: Do i need the internet to run this tool?
A: Yes, you will need internet to run this tool, as it will need to free up your activation credit.
Q: If I uninstall BioShock on my computer and re-install it again without changing anything, will I use up an activation?
A: No! As long as you have not changed any major hardware component, such as a motherboard, hard disc drive or DVD ROM drive, you will not be asked to re-activate BioShock as it will use the activation information (activation license) from your previous installation.
Q: So I can install and uninstall it as many times on my computer without using up all my activations if I haven’t changed anything?
A: Yes!
Q: What version of BioShock does this Revoke Tool work for?
A: This tool works for the retail box copy of BioShock. The Steam version of BioShock already revokes an activation when BioShock is uninstalled on a machine, and does not need a tool. This tool does not work for Direct2Drive.
Q: Can I install BioShock on the same computer under different user accounts?
A: Yes, although you will be asked to activate it for each user account, which will use up one of your activations.
Q: Will I be able to revoke the activations under each account and free up all the activations for each user account using the BioShock Revoke Tool?
A: No! Unfortunately, the revoke tool will only revoke the activations once for any given computer, the activations used for any additional user accounts will remain active.
Q: So how do I get these activations from multiple user accounts on the same computer back?
A: 2K Games are working on a solution for this with our activation partner, as soon as a solution is found we will make it available. For now, if you get stuck, please refer to the Exceptional Cases - Requests for Additional Activations section in the ReadMe document for more information.
Q: How many different computers can I install BioShock on?
A: Five, but each one will use up one of your hardware activations. For example if you wanted to install BioShock on your main desktop gaming rig and also on your laptop, that will count as 2 different hardware configurations and therefore use up two activations.