If you're married, your spouse will get hit with it.
It does not travel up (parents) or down (children) unless they co-signed for the debt. A co-signer is responsible for anything with their signature.
Your estate will be liquidated to cover the debt. Anything you own can be mandated to be sold to pay off your obligations. I can tell you, having settled a few estates, that you will be amazed at which companies will try to sell absolutely anything you have to try and get some money back. Any property of value that you give away close to your death may be recalled for sale.
Special rules for student loans:
If you have lots of student debt, make sure that whoever will get stuck processing your estate knows that the dept of education or your loan processor needs a copy of your death certificate to stop billing. It may take a few tries. They don't give up easily. Private loans may be not discharged and will go through the probate process.
If your parents have parent PLUS loans issued by the government, they will be discharged after you die. Private loans that belong to a parent will usually not be discharged if the student dies.
All of this sucks. There is quite a process to settling the estate of a loved one and it's a burden on whoever has to do it. Please have your bills organized and available, including those in collection. You can leave them in a drawer, but it's easier if people don't have to dig for them.
I'll be honest, I hate this reason for CTB. It seems to me like such a waste. Have you tried bankruptcy? It's not as bad as it seems. Just a thought. Best wishes, no matter what you decide to do.