I've heard that a grandparent can pay a grandchild's tuition directly to the college without any gift tax problems. Is this true?
Yes. The general rule is that any gifts over the $13,000 annual gift tax exclusion from one person to another are subject to federal gift tax and generation-skipping transfer tax (GSTT). However, an exception to this rule exists for certain tuition payments. Specifically, any tuition payments made by a grandparent (or anyone else) directly to a qualifying educational organization (e.g., a college) to cover a student's tuition expenses are exempt from federal gift tax and GSTT, even if such payments exceed the annual gift tax exclusion. The key is that such payments must be made directly to the qualifying educational institution. You will not qualify for the exemption if you gift the money directly to the student with instructions to apply it to tuition expenses. The unlimited exclusion does not cover books, supplies, or room and board expenses.
This type of gift may still be subject to state gift tax and/or GSTT. Call a tax attorney in your state for more information.