Every household has a point at which a repair stops being an inconvenience and becomes a problem. Only you know where that line sits. Before you read a single contract, find it. A service contract is a tool for one specific risk, and it is only worth buying if that risk would hurt your household, not just annoy it.
Start with the bill you would actually feel
Sit down with the last few months of statements and work out how much unplanned spending your account can absorb without pulling money from rent, groceries, insurance, or debt payments. If a sudden repair would not change what you pay for anything else, a service contract may be easing a worry more than a risk. If it would force a hard choice, the risk is real for you.
Separate the worry from the exposure
Worry about breakdowns is real, and it is not the same as financial exposure. Picture the worst week: the car is off the road, you miss work, you pay for a tow and a rental, and then the repair itself lands. Each of those costs has a size and a timing. A household with savings set aside can usually absorb a surprise. A household living close to the edge may not. Write the answer down so you know which group you belong to.
Check whether the car is worth the protection
If you are weighing protection for an older or high-use car, the bigger question may be whether the car is worth keeping at all. Compare the likely cost of repairs against the car's value and against your plans for it. Protection that outlasts your ownership plans can end up paying for something you never use. If you do decide to look at contracts, the providers sorted by money-back period page shows the published refund windows so you can compare what leaving early would look like.
Decide before the finance office does
Settle your answer before you sit down with the seller. Once a contract is offered as part of a financing package, the decision is harder to see clearly. Decide whether a surprise repair would hurt or only annoy you, and let that answer determine whether the protection is worth reading closely at all. If the answer is annoy, you may be better served by keeping the money in reserve.