Late payments and charge-offs, where creditors write your bill off because they have given up on you, are not allowed to remain on your report after seven years.
The same debt should not be listed more than once, particularly by more than one debt collector.
Your Spouse's Bad Debts
If your spouse failed to pay bills before your marriage or after your official divorce, as long as your divorce filing was handled properly, these should not be on your credit report.
Other People's Accounts
Other people's account information -- good or bad -- should never appear on your credit statement. A cynic might say to keep the stranger's entries if they are positive, but who's to know when that person will face a financial crisis that will ruin their credit, and yours.
Old Credit Applications
"Hard" inquiries where you apply for credit count against you. They shouldn't remain on your report for more than two years.
Credit For Which You Didn't Apply
If you spot hard inquiries that you didn't authorize, dispute them. "Soft" inquiries, where banks check your credit report in order to offer you a preapproved card, are harmless. Checking your own report is harmless.