If I die without a Will, will my children be responsible for any debts taxes, etc. owed by me?

No, your children would not be responsible for your debts or taxes. Your estate would be responsible for them--that is, these debts may have to be paid from whatever money or property you leave behind, before that money or property could be passed to your children. Worst case, you children might not inherit anything, if everything goes to your debts (and also final expenses, like funeral costs); however, even if those debts exceed your estate, your children will not be responsible for the balance. At worst, they will not inherit anything, but will not owe.