When a dealer offers you an extended warranty for a car you're buying, whether new or used, you don't want to be too quick to walk away from that offer. You might assume it's just their way of trying to make as much money from your purchase as possible, but in truth, it might be in your best interests to take them up on that warranty offer. Note when it's good to consider an extended car warranty for your car, even if it's a new model.
Note if it offers special features you may need
Some warranties offer more than just covering the cost of repairs; they may also offer roadside assistance and free towing if the car should break down for any reason. This can be invaluable if you don't have family you know you can call if your car should break down, or if you know you would never be able to change a flat tire on your own. An extended warranty can also cover body damage that would otherwise not be covered by your standard warranty; if you drive in city traffic and risk fender-bender accidents, this might be a good choice for you. By noting any special, additional features of that extended warranty like this, you can know if it would be useful to you in particular.
If the car model doesn't have the best track record for reliability
When buying a car, you may note its track record for reliability based on consumer reports and such figures. However, despite those facts and figures, you may still decide to buy a car that isn't always known for its reliability simply because it's all you can afford right now, or because it offers other features you need. Since your car may be more likely to break down in the future, you might invest in the extended warranty.
If the warranty would increase its resale value
If you know you'll want to resell the car sometime down the road, consider if the warranty is transferable and if this might increase the car's resale value. Being able to offer a warranty with a used car can sometimes be a good idea, since buyers know the car has already suffered some wear and tear. If they know there is a warranty that will protect them against the cost of major repair jobs down the road, you may see your car sell more quickly and easily than if you didn't have that warranty in place.