My elderly mother is living with me and wants to pay rent. Do I have to claim her rent as additional income on my taxes?

Legally, you are required to claim rent as income. Then you can also deduct all expenses related to renting. A good tax person will be able to help you with this. If she is just reimbursing you for HER expenses like food, utilities, toiletry, etc., then you don't need to claim the money as rent. To be sure, check with your tax guy/gal.