Yes, an employer can decide not to hire you based on information uncovered in a background check, especially if the company finds inconsistencies between the information you provided and what the background check shows. Certain criminal records can also cause employers to decide against hiring you.
If the potential employer decides not to hire you based on information from the background check, it must send you a notice of adverse action, share the report with you and give you enough time to dispute any inaccuracies.
Additionally, note that many states have passed legislation banning discrimination against people with criminal records, if the offenses they were convicted for are not directly related to the role they'd be hired to perform.
However, it's illegal for employers to base their hiring decisions on criminal records, evictions or credit history details unrelated to the job.