Yes, cancelation of debt is considered income and must be reported on your tax return.
Whether it is taxable or not depends on whether you qualify for an "insolvency exclusion" -- if you were "insolvent" on the date that the debt was canceled, you can exclude the amount of canceled debt up to the amount that you were insolvent.
An example, to make all of those words clearer:
On June 15, you had assets worth $150,000 (a house, a car, a checking account, personal belongings, etc.).
On that same date, you had debts of $160,000 (your mortgage, your car loan, a student loan, a credit card debt, etc.)
Because you owed more than you owned, you were insolvent by $10,000. ($150k-$160k)
If you had owed $15,000 on that credit card and they wrote it off on June 15, then you could exclude $10,000 of the canceled debt income and would have to pay taxes only on $5,000 that exceeded your insolvency amount.
If, instead, you had only owed $3,000 on that credit card, then you could exclude the entire amount because what was written off was less than the amount you were insolvent by.
There is lots more detail in this article: Guide to Debt Cancellation and Your Taxes
Be sure to pay attention to how to report this -- generally you'll report the entire amount canceled as Other Income and then report an exclusion of however much applies. Don't just leave it off your return, though, or the IRS will send a letter telling you that you forgot to report income.
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