It amazes me that anyone with even the slightest bit of common sense thinks that this can actually work. Let me just ask two questions...

1) How much of a pressure differential do you think it would take to suck wax out of your ear?
2) How much of a pressure differential do you think a burning piece of cloth produces?

As for the first one, I don't know but my guess is "a lot". Let's put it this way, if someone were to seal their mouth over your ear and suck, do you think they would get a mouthful of wax? Hell no. And do you think a candle can actually decrease pressure more than someone sucking on your ear? Hell no.

Not enough for you? Ok... Pressure and temperature are related by the ideal gas law, they are directly proportional. However, you're only going to get an increase or decrease in pressure when you change the temperature of a closed system. For example, if you warm the air inside a balloon it will expand and eventually pop. In the case of a candle stuck in your ear, this will not happen. The transfer of heat to the air will excite it, which will cause it to expand. This will create a pressure decrease near the flame where higher density air will rush into. Now, the problem here is that there is a small amount of air inside your ear and a large amount of air outside of it. Air is always going to take the easy way out, so air from the outside environment will flow in to fill the void.

The upshot is, a shop vac doesn't produce enough suction to get wax out of your ear (although it's probably enough to damage your hearing...), there's no way a burning candle will do it. Really, just take the damn candle and put it against your hand and light it. See how much pressure that generates on your hand...

In addition, this has been debunked by Straight Dope and Dr. Dean Edell (search http://www.healthcentral.com for candling). Both of them did tests and found that when the candle was inserting in a jar and an ear, the gunky buildup was the same. Straight Dope also had a subject try it and examined the ear before and after and found no wax reduction. So the whole thing is silly. In addition, melted wax and burning ash in the ear can be a very bad thing, so please don't try it.