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?