BatmanNate gives some good advice. Leaks are a no-no (unless the car is priced accordingly). Maintenance records are a big plus. Consider getting a month-to-month subscription to Consumer Reports' website. There you'll find reliability ratings and recommendations for used cars. It's really valuable, even if you think you know your stuff. 🙂
Make sure everything works, take the car through its paces for at least 10-20 minutes to allow it to warm up and come to operating temperature. Listen without the stereo to any noises in the car. Sometimes taking a gearhead friend with you can help immensely if you're trying to figure out what a squeak, whirr, grind, or rattle is.
If someone says "oh, that's a quick fix, you can just buy the part and put it in," make sure your running shoes are tied. This is a sign they're too lazy to fix SMALL problems with the car... it'll make you wonder what it takes to get them to do something about a problem that could really ruin the car. :Q
Once you find out which car you want, check the value of the car against others for sale in your area (try autotrader.com). If you find ANYTHING remotely wrong with the car, use that as a bargaining chip to bring the price down. Having a check for a deposit is a good idea, so a good find doesn't get snatched up from under your nose. If you're almost sure you want to buy it, but don't have or don't want to give a deposit, ask if the person selling it will give you the right of first refusal. That means you get first shot at the car if someone else comes in and asks to buy it.
Good luck. 🙂