My 18 year old daughter lives with me full time, is full time high school student, has had a baby 12/5/07 and the baby also lives with me. I do claim my daughter as a dependent. The baby is covered by his fathers insurance. Who claims the baby as a dependent on their taxes, the father or myself?

These are the two main requirements for claiming a dependent under Qualifying Child:
1. The child must have lived with you for more than half of the year.
2. The child must not have provided more than half of his or her own support for the year.
So it does not matter you provided the support for the child. Only you can claim your daughter and her baby.

It is better that you discuss your position with the father of the baby. If both of you claim the baby, you will get letters from IRS. One of you will have to amend the tax return and pay interest and penalty of the amount owed.

MukatA is correct. You can claim the baby as your dependent UNLESS your daughter made over $3,400 in 2007, in which case it might make sense for HER to claim the child (because of the Earned Income Credit).

The same logic applies for the FATHER claiming the child, though that would be illegal because the child is living with you, not him. Best to dcuss this with him before anyone files.

If the father claims the exemption, he needs to attach the custodial parent's written declaration (Form 8332) that she will not claim the child as a dependent for the year, and the noncustodial parent attaches this written declaration to his or her return.

Agreed, but the IRS will not know about the custodial arrangements, so NOT attaching the Form 8332 will have no consequence unless two (or more) people claim the child.

It is always safe for the noncustodial parent to get Form 8832 signed before claiming the child. This will avoid any future problem and interest and penalty.

Agree with MukatA; attaching the Form 8832 is never a bad idea.