Since we relish blowing out birthday candles, I started there. The tradition of putting candles on birthday cakes started with the Ancient Greeks, who put candles on offering breads in ceremonies to the Goddess Artemis so the breads would glow like the moon. This also allowed prayers to be carried up to the Goddess in the smoke of the candles. There is no indication of how these candles were extinguished and no lasting tradition that demands a ceremonial breath to do the job.
Blowing out candles when making a wish seems to be a relatively modern tradition. Many of us these days believe that blowing out all of the flames with one breath poses just the challenge that the person of honor must accomplish to win the manifestation of their wish. We say, "If you don't blow them all out, your wish won't come true." Joke candles that will not blow out are made to thwart the efforts of this superstition. This bit of mundane magic actually glorifies the act of blowing out the candle. Since the Church has pushed many "paganisms" into being simply superstitions, I am confused how the idea that we must blow out candles has survived, despite that many Pagans are saying one should not.
Except in very specific occasions, many Jews do not blow out a candle flame because it represents the soul. There are numerous bulletin board entries of worried Jewish mommies asking if they should allow their children to blow out birthday candles, and numerous responses by people, who claim to know all about Paganism, saying the practice is Avoda Zarah, "foreign worship." Doing so threatens to recognize the rituals of other faiths; it amounts to idolatry. Frankly, I've found that most Judeo-Christian people enjoy working way too hard to find as much dogma as possible to structure their lives, but I commend the strong drive to be true to one's faith. If their souls are truly in danger, I ultimately don't see how snuffing out a soul is any different than blowing out a soul.
Conversely and because of the same symbolism, Buddhists prefer to blow out their candles. The idea is that extinguishing a flame hastens reincarnation because it represents helping a spirit to move out of this incarnation.
Gerald Gardner made no mention of a blow-out prohibition in the fiction work High Magics Aid (1949) or in the nonfiction classics Witchcraft Today (1954) or The Meaning of Witchcraft (1959) that began much of contemporary Wicca. I also found no mention of it in any of the works on my shelf by Buckland or the Farrars, so it seems that it is an element that is not a part of Garderian Wicca, but that trail may simply be beyond my current research. Certainly possible is that this may be something that was only part of the oral tradition - told from teacher to student. This would make it a great way to identify an inexperienced or false witch.
The earliest mention I could find was by Scott Cunningham in his 1991 book Earth, Air, Fire & Water in which he states that he (personally) doesn't like to blow out candles because he feels it is an affront to Fire (102). Based on his word choice, it seems that Cunningham invented the prohibition. But why?
Cunningham actually received his witch training from Raven Grimassi, a practioner of Italian witchcraft known as Strega. The Strege place enormous emphasis on the hearth and the fire within it because of what it meant to the pagan family, village and people. They have moved a symbol of the hearth to the center of their altar in the form of the "spirit flame," which is a bowl of alcohol burning blue to represent the spirit of the old ways, the power of life, and the presence of the Deity. Great reverence is given to the spirit flame and it is never extinguished - it must be allowed to burn out. I believe that Cunningham's contact with Grimassi infused him with this reverence for fire and led to his unwillingness to blow out any flame.
Since all candles have to be put out somehow, here are my thoughts on the topic.
2. Snuffing out a candle requires an extra tool on the altar, or you must run the risk of finger-snuffing incorrectly such that you burn yourself. If you are a minimalist or pragmatist, you might choose to blow.
3. The idea that the element of Fire would be disrespected by being overpowered by the element of Air is a stretch (sorry, Scott). Firstly, since the elements make up all things, even snuffing would be an affront to Fire by overpowering it with water or earth. So what's the difference? Secondly, fire can't exist without earth (the candle wax) or air - the flame is a harmony of fire, earth, and air.
4. If you really think that blowing out a candle blows away the magic, then you don't believe your magic to be very powerful. How will you possibly defend against any curse when your magic can be so easily overcome by a puff of air? Is that much doubt present in your mind?
UPDATE: April 28, 2015
Adonis Merlin, a very respected reader and teacher, discovered some information recently that might make this topic a bit more understood.
In 1942, Henri Gamache wrote a pamphlet revealing some Hoodoo candle burning practices, which he titled "The Master Book of Candle Burning: How to Burn Candles for Every Purpose." In this short missive, he discussed that many Hoodoo candle spells are done in parts, during which a section of a candle is burned at intervals over the course of a day, several days, or nights. It is imperative during these intervals that a candle be snuffed out, not blown out, because blowing out a candle signals the conclusion of the spell.
Similarly, James Frazer's "The Golden Bough," which is taken as one of the most important and guiding works to pagans of the last century, reviews the use of "perpetual flames" by classical pagan cults. These were flames that were either fed by devotees or by a natural source such that they would never extinguish from lack of fuel. In those cults, the act of letting such flames go out was considered a very malevolent omen and so great lengths were taken to avoid losing the flame.
It should be noted that some older Wiccan spells (those written before all this angst over puckering up and blowing) actually indicate that their candles should be extinguished specifically by blowing them out.
I stand by my previous "compromise" above: those candles used for spells that do not conclude in a single session, or are novenas for saintly or spiritual prayers, should be snuffed out. All others can be blown out. Perpetual flames, of course, should be allowed to burn at all times.