Under current US tax code, you can receive $14K from an unlimited number of people with no tax consequence to them.
Yes, the burden is on the giver.
There's an exception to most rules. If I gift you a large sum and don't fill out the required paperwork, paying the tax due, the IRS can go after the recipient for their cut. "Follow the money" is still going to be applied.
Even if over $14K, a tax isn't always due. Form 709 is required, and will allow a credit against one's lifetime gifting, currently $5.34M. In effect, the current limits mean that 99%+ of us will never worry about this limit, just file the paperwork.
Last, the 529 College Savings accounts permit a 5 year look ahead, i.e. a parent can deposit $70K to jump start her child's account. Then no gift for next 4 years.