In more detail
Common forms are a personal loan, a 0% balance-transfer card (usually with a transfer fee and a promotional period that ends), and borrowing against home equity. The test is total cost, not the monthly payment: compare the new APR with the weighted average APR of the old debts, add any fees, and keep the term no longer than you would have taken anyway. Turning unsecured card debt into a loan secured on your home lowers the rate but puts the home at risk.
Why it matters
A lower monthly payment can hide a higher total cost when the term is stretched. Consolidation also fails if the cleared cards are run up again, leaving the new loan plus fresh card debt.
Example
Cards of $4,000 at 24%, $3,000 at 19% and $5,000 at 22% have a weighted average APR of 21.92%. Paying each off over 36 months costs $457.85 a month and $4,482.66 of interest. One $12,000 loan at 11% over 36 months costs $392.86 a month and $2,143.13 of interest; with a 3% ($360) fee, $2,503.13 in all, a saving of $1,979.53. Stretching the same loan to 60 months cuts the payment to $260.91 but raises interest plus fee to $4,014.54, almost wiping out the gain.