My mom wants to give each child $15,000 a year to care for her. Any tax problems with this?

Gifts up to $14,000 in 2013 are not taxable for gift tax purposes (they are never taxable for income tax purposes, regardless of amount). The additional $1,000 per child could be taxable, although your mom can apply part of her lifetime exemption ($5.25 million in 2013) to offset this additional gift with no current gift tax. However, if you and your siblings are obligated to use the funds for your mom’s benefit, then there is no gift and no tax consequences.