Consider this: public records may or may not be online. It often depends on the resources of the state or county from which the records originated. You may have to request information via a form, over the phone, or go to a physical location such as a court house for the county you are interested in to actually see the records. Check online first, but be prepared to call or travel to the location if necessary.
Public Records and Libraries
Libraries typically do not have any more access to public information than you do. However, libraries do subscribe to specialized databases that help with some kinds of proprietary information, such as corporate & industry profiles. And don't forget, librarians can help you navigate and find what you need, even on the Internet -- we're used to searching for information, so don't hesitate to ask a librarian for help!
Confidential or private records
Public access to records such as employee records, student transcripts, patient health records, etc. may be restricted by the agency holding them or you will be required to have a FOIA request.
You can usually always see your own records by request with proof of identification.
Other good sources for finding public records
Large public libraries (usually have good local historical & genealogical sources - print and online)
City Hall of any municipality
State agencies such as Dept of Health, Dept of Motor Vehicles