Google "ohio debt statute of limitations": ohio debt statute of limitations - Google Search The first few results will give you what you seek. Wow - it appears to be 15 years for signed contracts, 4 years for open accounts. I believe -- but am not certain -- that credit cards fall under "open accounts".
How did Dumb Bob know you were thinking about Ohio? Perhaps he should do a magic show. It seems like Ohio is different, if Dumb Bob recalls right, probably because of that really long SOL on written contracts. You'd probably be wise to read your state's case law on this.