If your background check reveals that you have a criminal history, or some other undesirable quality, employers are within their rights to not hire you. Of course, employers should be fair minded when making hiring decisions. They do have a right to check their employees backgrounds though, for their own security.
In today's world, I believe that background checks are vital for ensuring that individuals are being honest about their work experience and their criminal background before getting a job. If people are working with big data, medical records, vulnerable populations, or in other sensitive areas, it should be required that they pass a background check prior to employment.
Yes, I agree that a background check should prevent you from getting a job if something is found in the background check that would suggest unsuitability for that position. If a minor crime was committed in someone's distant past, this should not affect their current employment opportunities. However, if a more serious crime has been committed or crimes were committed more recently, that could suggest that the person in question may be a liability to any employer and should not be hired.
If the crime in question is reasonably relevant to the job then they should be able to inquiry about it. This should be spelled out in the law.
A person's entire career shouldn't be ruined just because they committed a crime at one point. Not only is that bad for themselves it's bad for the rest of society. They may be tempted to turn back to a life of crime because they can't get any good jobs.
There are some jobs that deal with sensitive issues like banking or any job involving national security secrets. Those jobs should make sure there are no crimes on their record like "hacking" or "embezzlement".
I do not believe that a background check should prevent a person from getting a job. Employment is important. A necessary part of life for almost everyone. It is unfair to deny someone the ability to make a living due to the mistakes of their past. If the past crime in question has a close relationship to the work that the prospective employee would be engaging in, there would be just cause for hesitation. Other than that, it shouldn't necessarily interfere.