It depends on what is included in the background check. A criminal background check can take 1 to 3 days to complete, depending on the county and whether their records are digitized or on paper. The reference checking can take longer, depending on how long your references take before they return the call(s). And the fact checking on your education and experience also depend on people at the other end of the phone line answering the phone or returning the call(s).
Bottom line, a thorough background check can take a week or more if HR is rushing it, and following up on the missing pieces daily.