I've never had a problem finding a gig even though I'm a felon, but I don't work with BigCorp because that's not my scene (and it's probably harder to market myself as a felon to anyway):
At the end of the initial phone call / screening, I tell them, transparently: "there's no way I can pass a background check by the way"
It has always been well received, even to recruiters and head hunters.
I'd say the industry type and company size matter a great deal. Felons are legally barred from working at any FDIC insured company. So forget banking/finance. Also healthcare will also have stringent background checks. Giant corporations may have policies that immediately skip over you regardless.
I'm not sure how I've made it really. Luck mostly. I'm ten years removed from my arrest and it still comes back to haunt me.
How does it work? Will the background check reveal what crime was committed, or just that you are a felon? I could imagine knowing the specific crime could influence the final decision on hiring or not, no?
We are a finally regulated company though, so the requirements are perhaps a bit more strict.
If you explain all of this ahead of time - much like this website does - then we can take it into account and there won't be any surprises. For a serious offence, it's probably still going to be a no. For anything fraud or white-collar related, it's going to be a no. But for less serious offences not related to our business, I think we'd be reasonably comfortable.
I can see how you would want to first be judged on the merit of your skills and then an employer might be willing to make a judgement call in your case, after they have judged your value.
As opposed to your resume being thrown out without even as much as a second thought if you are a convicted felon.