Personally I never had any convictions, but my ex wife prior to the finalization of our divorce use to live in a home that she was evicted out of, and that eviction shows up on my credit report.

Some landlords have a strict no-criminal-record policy, and will refuse to consider anyone convicted of a crime. 

No jury would convict me. 

Landlords who don’t want tenants who are going to mug their neighbors or deal drugs will now be treated as racists and potentially sued.Last week, the Department of Housing and Urban Development issued new guidelines to landlords, warning that bans against renters with criminal convictions violate the Fair Housing Act because they disproportionately affect minorities.In effect, the Obama regime is now outlawing criminal background checks for apartment rentals, even though such screening is critical for the protection and security of tenants and property, and serves a legitimate business need.In a newly released 10-page missive, HUD warns landlords they can be held liable for discrimination if they deny housing over criminal records.

It ends up that the prospective tenants have no criminal convictions, nor expungements, etc.

It's important to look at a nationwide report because they might have been convicted of an offense or be on a sex offender list in another county or state and you deserve to know that before renting to them.Another powerful screening tactic is to get an address history report so you can compare their actual residential history with what they claim on their application.  

Have any of you guys ever known anybody with a felony conviction who was able to get licensed, preferably in Ohio?

Ask your self, would you rent to a convicted criminal?

What if they have convictions in another county or state though?  

Saying that with conviction should be enough to convince most otherwise responsible applicants/tenants to abide by that clause.