If you happen to cosign a secured loan, as on a house or a car, you can be in a big pickle. The bank has the right either to demand that you pay off the debt or to take away the goods. Should you pledge your own property as collateral, the bank can take that, too. Cosigning for unsecured debt, such as a credit card, isn't as ominous, but even so, the issuer can sue you or garnish your wages in an effort to be compensated.
When you're asked to cosign on the dotted line, try to understand why the person can't get approved on her own. Is it because the bank knows something you don't? Perhaps she has a history of late payments. Maybe she hasn't repaid her student loans yet. Think about it: If you're being asked to cosign because the lender or card issuer needs "insurance," that's a flashing warning signal. These people are in the business of giving out money, and they don't make a profit by turning down prospective clients. So if a financial institution is reluctant to give your friend or relative the loan, you ought to be just as cautious.