You can re-light a candle without touching the wick. All you have to do is touch the smoke to a lighted match and the wick will re-light. Watch this video.
Here is why it happens: smoke contains a lot of the unburnt fuel and as it travels upwards, it mixes with the oxygen. The third piece required to make the candle light is heat. And that is what the lighted match supplies. Once the heat mixes with the smoke, it travels back down the smoke to the wick and the candle will light.
Science can be so trippy!