First, there are two classifications of background checks:

Consumer Report

A background check is classified as a consumer report if the purpose of the background check is to serve as a factor in eligibility for credit, insurance, employment or any other purpose authorized under Section 604 of the Fair Credit Reporting Act (FCRA).  This type of background check can only be obtained with the authorized consent of the person who is the subject of the investigation and therefor can contain both public and non-public information such as criminal records, credit report, driving record and various verifications of previous employment, education, certifications, etc.

Non-Consumer Report

If a background check is not going to be used for the purposes listed above, it is not a consumer report, does not need the consent of the subject, and is mostly limited to public record information.  With few exceptions, this means criminal records, which can be obtained by visiting your local courthouse. 

For a consumer report, definitely yes.  Just make sure you select a reputable firm by calling them to discuss your needs.  If they do not offer their phone number on their site, they are not reputable.  If you are an employer, seeking employment related background checks, one of the best firms in the industry is Abso.

For non-consumer reports, maybe.  You need to consider the value of your time, as you can get the information for free (in most counties) from the courthouse.  All you need is the persons name, date of birth, and knowledge of the counties for which they have resided for the past seven years.  Obviously, if the subject has lived far from you, your not going to be able to go to the courthouse yourself, but you can call the court and ask if they will check records over the phone (most will not, or will charge for this service), or they may be able to provide you contact information for a local court researcher that will perform the check for a small fee.  If you proceed to buy a background check on the internet be advised that most do not offer phone support, refunds, etc, and that most do not even check the courthouses.  Instead they use databases, which do not include data from a lot of counties.