Your dog runs out of the house and viciously attacks a neighbor who was walking nearby. Your neighbor sues you to cover her medical bills, lost wages, and pain and suffering.
Your daughter gets into a fight at school and punches another girl, breaking her nose. The girl’s parents sue you.
You cause a 10-car accident and your auto insurance property damage coverage isn’t high enough to replace all 10 accident victims' vehicles. Nor is your personal liability coverage high enough to pay for their medical bills.
Your teenager throws a party at your house while you’re out of town. Someone brings alcohol to the party, and one of the guests is arrested for driving under the influence on the way home. You are sued.