Spousal debt: Arizona, California, Idaho, Louisiana, Nevada, New Mexico, Texas, Washington, and Wisconsin.
Other debts: About 30 states have archaic, rarely enforced laws that can make adult children legally responsible for their parents' unpaid necessities, like medical or nursing home bills.
IANAL and this is a summary from Google, so I cannot vouch for the accuracy of any of it. I can just tell you that in my experience, NY does not pass on debt to spouses.