It would depend on how long a conviction stays on your record. Some countries give you a clean certificate if the offense is a certain number of years old. My understanding is that the only way to get rid of a felony conviction in the US is to have your record expunged. But this can only be done in certain circumstances. So if you apply fro a police clearance in the US right now, your conviction would be on that certificate. So any form of visa that requires a police background check from the US is ruled out.
that over the last year or two, you must have personally answered this question to people at least a dozen times. Perhaps you can pin this one or something.