My father died January 1, 2011. I filed the 2010 return as a joint return for my mother. This year we have received several 1099-c that were for credits cards that my father used for his personal business. They were all in his name, not my mothers. First, do I still need to file a joint return this year? Social Security did pay that first month in Jan. 2011 for my father. Second, if I do need to file jointly, do I have to include these as income on the return.

Your mother filed joint return in 2010. For 2011, she can still file joint return or as married filing separately.
On joint return the liabilities are limited. If she file separate return she may be able to ignore 1099-C. Let us see what others have to say.

If the Forms 1099-C represent a SIGNIFICANT amount of debt, then your mother MAY want to file a Married Filing Separate (MFS) return, and your father's estate will file his MFS return, with the executor of the estate signing the return.

If taxes are owed on the MFS return, the estate must pay those taxes BEFORE any of the estate's assets are distributed to the heirs.

The tax professional who is handling the estate tax returns should model the return both ways (joint versus separate) to determine which is the best way to file for the benefit of the family overall.

Thanks for replies! I have one 1099-c that is noted with his SSN and one 1099-c that is noted with his Ein for his business.

In both cases, the 1099-C imputed income would go on your FATHER's return (if filing separately).