Be very careful about who you buy a warranty from. I bought one on the last car I owned, and not knowing anything about them, bought one from an aftermarket (3rd party) provider. Knowing what I know now, I think the OEM ext warranties are better generally speaking.
Make sure you know what the deductible is for the warranty (usually anywhere from $0 - $100), and find out whether it's per-visit or per-issue. If it's per-visit, then you can show up with a laundry list of things that need to be fixed and they'll do them all for one fee. But if it's per-issue, they will literally charge you a deductible for every single thing that needs to be fixed. That can get expensive very quickly if your vehicle frequently needs repairs.
Also, make absolutely sure you look at the list of what's not covered by the warranty. Some of them have a long list of things that are not covered, and from a financial standpoint, that makes it very difficult to recover your money on the investment unless you have a serious problem like needing a new engine, transmission, etc. To me, if I'm gonna spend the money on an extended warranty, it better be exactly like the factory warranty in terms of coverage and out of pocket costs.
Lastly, find out what happens if you sell the vehicle before the warranty period ends. Some of them will give you a portion of your money back based on how many claims you've had. Some are also transferable, which may be a decent selling point if you're going to sell it private party.