The general rule is that all debts must be paid before assets are distributed. Your outstanding credit card balances, for instance, will be paid before any money or gifts are distributed to your heirs.
A major exception to this general rule is for "secured debts," such as home loans or auto loans. In the case of secured debts, property can be distributed with its debt. In other words, let's say you have a car worth $10,000 and have a $5,000 loan on the car. You can leave the car to someone, but it will be that person's obligation to pay off the loan.
What happens if you owe more than you own? In general, people cannot inherit another person's debts. If there are not enough assets to pay your debts, then all property will be sold to pay as much of the debt as possible, and no one will inherit anything.