Bioshock fans have been waiting for an announcement about when the promised sequel is due, and so far have loosely gotten confirmation that it's due before the end of this year with a short trailer released in October 2008. More interesting that the upcoming sequel, however, is news that 2K is apparently envisioning upwards of five Bioshock installments. Christoph Hartmann, president for 2K, has stated that they do see a logical way to, if done properly, release multiple sequels in the future for the game.
Mr. Hartmann is apparently wary of running the series too dry, ending up like some other mass-produced and mass-advertised series. While he won't name names, he sites certain series that demonstrate how large numbers of sequels can simply dilute things, becoming just a cash cow. Whether or not they can pull it off remains to be seen, and likely the success of the upcoming sequel, Sea of Dreams, will tell a lot about how "fresh" the series can remain.
That's not to say it can't be done. There are many successful series that had at least three if not more installments, such as the very famous Final Fantasy series from Square Enix, the Ultima series from Origin/EA and even more modern-day examples like The Elder Scrolls series, The Sims and many others from all genres. He does make a good point at being careful not to dilute things. It's difficult to do, and even if they are producing fresh content with every iteration, it's still very easy to fall into the "it worked last time, let's do it again" trap.