When you buy a used car, you should check whether the car has a warranty on it that is transferable. Of course if the car has an effective transferable warranty on it, the seller will probably throw that fact out there as a bargaining chip. If the used car's warranty is transferable and has a sufficient number of miles/time duration left on it, then you are covered, though you may want to consider purchasing an additional warranty. Be sure to get all the warranty documents from the used car seller before finalizing the transaction.
Now if you bought a used car and it is not under warranty, then it is possible to buy one for it, provided the vehicle is not too old or has too many miles, however finding this warranty can be difficult.
A used car warranty is basically a type of extended warranty. Considering that most used cars are sold past the initial grace period where "normal" mechanical failures are unlikely to occur, it is generally recommended to purchase a used car extended warranty. Costs can range dramatically and some warranties may cost as much as 50 percent of what you paid for the used car.
Similar to insurance and financing contracts, warranties require attention to the fine print. If you are looking for a used car warranty and the contract does not contain "wear-and-tear" as part of its coverage, then it probably is not worth it. What this means is that warranty companies will only cover mechanical failures, and not failures that are the result of a buildup of "normal" wear-and-tear. Some warranty companies will try to leave out this wording so they have a gigantic loophole to saunter through come time to pay the claims.
You should probably crunch some numbers before actually purchasing a used car extended warranty. If the used car you bought is cheap and you intend on driving it into the ground, then purchasing a used car warranty may not be worth it. Also, if the likely-to-be-necessary repairs on the car will be cheaper than what it costs to extend a warranty, then you are not saving any money by going with a used car warranty. Of course, if a breakdown does occur, there is always the roadside assistance and towing that frequently comes with warranties.
Things to be Aware of:
Some used car dealerships will mention something like an "as is" used car warranty. For all intents and purposes, this means that you do not have a warranty at all. Any buyer's guide that comes with a used car should indicate clearly what the words "as is" implies.