When shopping, check that the wick is tightly braided and feels secure (give it a tug). Loosely twisted or poorly anchored wicks cause candles to burn unevenly or flames to flicker wildly, potentially igniting nearby items. Inspect jars or votives, too. Thicker glass is less likely to crack. For any, read the label for recommended burn times and a "Keep out of reach of kids and pets" warning. Including this info is voluntary, but it's a sign that a company cares about safety.
Up to snuff
To put out candles, use a candle snuffer (find one for less than $3 on Amazon or at IKEA). Or, when (gently) blowing out any candle, place your hand behind the flame to keep wax droplets and smoldering carbon from scattering.
Mind your measurements
Trim wicks to 1/4 inch every time you light them. A short wick means a more controlled flame. A flame should be only an inch or two high, and steady. Lots of flickering may mean the candle is in a draft and should be moved (or that it's of poor quality), and too high a flame is a fire hazard: Toss the candle.
Location, location, location
Never leave burning candles unattended, and always put them on heat-resistant plates or in stable holders. Avoid holders that seem top-heavy, as well as candles that wobble and could topple over (dripping wax into the bases won't do the trick). Place candles so their flames are at least three inches apart (to keep one from melting another) and away from flammable decor (drapes, garlands, etc.) and walls (to avoid soot stains).
Watch the clock
Don't burn pillars more than one hour for every inch of diameter longer, and the pool of liquid wax can get so big that the candle can lose its shape and spring a leak. And never burn any candle (except tealights) all the way down, lest the surface underneath be damaged. Throw out tapers and pillars when they're within two inches of the holder, and jar candles that are within a half inch of the bottom.
Got a half-burned jar or pillar candle with a hard-to-reach wick? Prevent singed fingers by lighting the end of a piece of dry spaghetti to use as a long-handled match.