I've had good experiences with all the used cars I've ever owned, all four of which were GM cars. Here are my rules for used car buying:
1) Buy only a car which is at least 6 years old -- inexpensive financing is available for used cars up to 5 years old, which artificially inflates the price.
2) Buy only from new car dealers. Their used car selection consists of trade-ins, generally from drivers who are sufficiently responsible and competent to be able to afford to buy a brand new car. More importantly, new car dealers nearly always get rid of all their 6+-year-old trade-ins via wholesaler buyers, who come by every week or two and haul away a big collection of them, no warranty, no questions asked, for prices well below book value. This means that you are in a VERY strong negotiating position re price, especially when you are paying cash.
3) Decide on one or two models/years/mileage ranges that you want, and comb newspaper and online ads for the absolute lowest prices on the models/years/mileage ranges in question, that are not described as half-totalled from a crash, and write those model/year/mileage price combos on a card in ink (yes, you are still going to buy from the new car dealer).
4) Go on a major online car search engine like www.cars.com that will give you the listing of specific dealers in your area, so you can then contact the dealers directly. Pick out the car you want at a dealer close enough to you. Pick out your second and third choices too. Don't pay the slightest attention to the prices advertised. Write this info down on your price card, next to the applicable model/year/mileage/price info that you previously wrote down. Make a mental note of the price that you wrote down in ink that fits the corresponding model/year/mileage description, and call up the dealer who is advertising your first choice car.
4) Tell the salesman upfront that you do NOT want a warranty. That knocks a bundle off the price right there, and you can use the savings to pay for any major repair that might be needed. If it turns out not to be needed, you keep the bundle. Tell him also that you will pay with a cashier's check, will pay and pick up the car today, and that you will pay $_____ (the amount you wrote on your card). Do not under any circumstances budge by a penny, or give any indication that you would even THINK of budging by a penny, and refuse to discuss any other cars the dealer has available. He wants to make the sale, he and his manager know perfectly well that the car will be going out the door for a lot less than you're offering within a few days, and they will play the "I'll talk to my manager and see if I can get him to come down a little more" game for as many rounds as you'll hold out for. If by some chance they don't submit to your will within 10 minutes, end the call and proceed immediately to the #2 choice on your list.
In my experience, it is very easy to get a nice used car for less than 50% of what the dealer advertised it for. The last time I employed this method was almost 6 years ago, and I'm still happily driving the car that was advertised for $7950, which I paid $3500 for, and which has yet to need a major repair. If it had turned out to need a new engine or transmission, I'd still be out less than the asking price, even if the repairs had been needed well after the usually short warranty on a used car would have expired. Happy shopping!