EPIC has a great roundup of the privacy implications of the surveillance and control technologies in use at America's themeparks:
The personally identifiable information collected in the form of a digital scan of visitor's fingerprints is associated with a guest's pass. The fingerprint scan information is used to limit access to the theme park to only those who have purchased tickets or entered the park with a particular pass.
Unfortunately, many visitors to the theme parks are not aware of the new policy. They are not informed that their fingerprint information has been scanned and retained. Customers were not provided with information on how long the fingerprint information would be retained, nor whether the information collected would be used for other purposes other than the control of admission to the theme park.
(via Schneier)
Update: Looks like EPIC got some of this wrong. According to articles like this one, Disney only scans hand-geometry, not fingerprints. (Thanks to Kevin and many others!)
