In the state of Colorado, there are no requirements to keep any specific borrower information. However, if your library stores the information, it could be required, by government authorities, to turn over the records it has.
Exactly how much circulation information is stored varies library by library. The integrated library system (ILS) we use provides a couple of different options. We store everything the borrower has currently checked out. Once the borrower checks that item in, it comes off their checkout record. However, their name stays associated with the item record until the next borrower checks the item out (this is in case we discover the item was damaged or is missing a DVD, etc). In addition, we have the option to store additional checkout history if we wished. The version of Horizon we use provides the options to only keep the basic circ history (detailed above), provide an opt-in for individual patrons to keep their circulation history, or turn on circulation history collection for all patrons.
Of course, we also have database backups. So, while technically checkout information disappears from the patron records as soon as it gets checked in, in reality we do have a set number of days in backups that would contain additional checkout information.
Regarding who has access to this data:
This tends to vary state by state. ALA, the American Library Association, has a page that offers links to various state laws: http://www.ala.org/offices/oif/ifgroups/stateifcchairs/stateifcinaction/stateprivacy
Colorado's statute is as followers:
Colorado Law 24-90-119. Privacy of user records. (1) Except as set forth in subsection (2) of this section, a publicly-supported library shall not disclose any record or other information that identifies a person as having requested or obtained specific materials or service or as otherwise having used the library. (2) Records may be disclosed in the following instances: (a) When necessary for the reasonable operation of the library; (b) Upon written consent of the user; (c) Pursuant to subpoena, upon court order, or where otherwise required by law; (d) To a custodial parent or legal guardian who has access to a minor's library card or its authorization number for the purpose of accessing by electronic means library records of the minor. (3) Any library official, employee, or volunteer who discloses information in violation of this section commits a class 2 petty offense and, upon conviction thereof, shall be punished by a fine of not more than three hundred dollars.
Note that even parents don't have access to their child's record unless they have their child's library card or number.
My understanding, and I'm not a lawyer, is that Federal laws don't say who can't access the record but rather who can. One of the big debates within library circles for the past decade deals with the USA PATRIOT act. Basically, in certain circumstances it allows Federal authorities to have access to library records without a court order. See the references below for more information.