My current car is a used car, thing is, I bought it from the garage and it came with 1 year warranty. Buying just from random people can be a risk for sure, but if you buy a used car from a garage or dealer, they will check al the important things. Depending on the age of the car and the company you're buying it from, it might have warranty. Here, in The Netherlands, they even have branch organizations, so if a company has this sign you know they need to meet certain standards. I have my second hand car for 11 months now and haven't had any problems at all. A friend of mine, who bought a second hand car from a random person she didn't know has had nothing but problems with the car which was bought later than mine.
My advice: go to a respected company that sells second hand cars, look at the age of the car and the millage, check the car yourself and ask for warranty and a test drive.