This is a very good question! Unfortunately, this is not an easy answer. It really depends on the felony. Most states are cracking down on felony convictions. However, they are willing to listen. This is really a state by state issue and again…it depends on the felony.
For example: if you received a felony in Arizona for a DUI most states will still license you including the state of Oregon. I would recommend having a detailed letter explaining the circumstance when submitting your license application.
If the felony is for fraud, embezzelment, and the likes your chances are slim. Before starting the daunting task of completing a license application it’s always a good idea to speak to the licensing regulator of the state you are interested in getting licensed in and ask them before you apply. You may want to speak to the licensing supervisor and ask them if you can submit your package directly to them if they indicate the felony will not be a problem.
I would also recommend providing a cover letter addressing who you spoke to and inform them of the felony and the attached explanation. The licensing divisions in the various states speak to many people every day so the more you document the better off you will be.