One of the most popular posts on this blog is the post about reading smoke omens on candles. Many people who find the blog through that post write asking about the meanings of other kinds of unusual burn patterns from candles.
I should mention here that while certain burn patterns have a "traditional" meaning, I do not actually find all of these to be true or reliable. In fact, the only thing I've found to have a consistent and reliable meaning of any sort, is if a candle goes out prematurely -- that is always inauspicious and indicates the work is really having a hard time coming through. Unless you're dealing with a defective candle, it probably means that it will not come to pass.
Some other common phenomena that are used to read omens are:
Candle burns clean, with little to no residue or remaining wax. As I was taught, this is desirable and a sign that that spell has taken and that there is nothing "left behind" to create further obstacles or that needs more work. However, there are some traditions that see this as the opposite -- that a good candle should drip and that a clean burn means someone is working against you because there is "nothing left" of the spell work you performed.
The candle drips wax which makes a shape. My experience is that one shouldn't spend too much time looking for ominous shapes in the wax. If the shape is genuinely significant, it will be obvious and apparent -- you'll look at it and it will just pop right out at you that it's the shape of a flower or a hand or whatever. Meaning, of course, must be interpreted in context of the shape and of the spell's intention -- for example, getting a perfect heart shape would be a good sign in a love spell but a bad sign in a breakup spell; in a protection spell it might be a sign to take courage or a reminder that your loved ones will help to protect you; in a money spell it might be a reminder to work with love and care to gain money or a suggestion that a loved one might give you money; in a jinx spell it might indicate the victim will have either heart trouble or romantic misfortune depending on the severity of it. Some more info about interpreting shapes can be found from this post.
The candle crackles, sputters, or makes other noise. It's usually agreed that this is an effort to get your attention being made by the candle or the spirits or whatever entity you believe is aiding the work. They might be trying to notify you of a problem. It's also possible that you have a candle which became wet at some point, as scientifically speaking it is dampness or other contaminants in the wick that create this effect.
The candle flame flickers. Scientifically this usually either means that you've put the candle in a breeze, or that there's getting to be a buildup of liquid wax that's threatening to drown the wick. Mystically, it can mean there's trouble or opposition to the work.
The candle flame burns very hot, large, and becomes a fire hazard. Definitely a bad omen, and commonly held to mean someone is working against you. I recall two particular cases where such things happened to me and in both of those, the trouble seemed to be that the work itself was in some way problematic -- a confused intention, or something the target of the spell was greatly opposed to.
Pieces of wax break or fall off as the candle burns. Said to indicate separation in some form. The most interesting experience I had with these, was an incident where I was doing work for a client burning candles against someone who was believed to be another magical practitioner. At some point a piece of wax came shooting off the candle, flying right at me. It was shaped like a hand flipping "the bird". It was almost certainly a sign that the other witch sensed what was going on and was sending a message.
In the end, "weird" phenomena is more likely to be significant than something that happens routinely. If your candles usually burn hot or usually drip a lot of wax then that is less likely to mean anything in particular. Also, one should avoid putting too much stock in an omen until after the spell is completed -- I often get questions that go approximately "I'm burning a candle and it's burning smokey/hot/low/flickering, what does it mean?" If this is happening, wait till the candle finishes and you might have a clearer sign.
One confusing matter is if you are burning multiple candles in a spell and they all burn in different ways. In such cases, try to account for what each individual candle was supposed to symbolize.
Also take into account that freestanding candles have to be read differently from glass-encased candles. Obviously glass-encased candles cannot drip or break off pieces of wax, and flickering is usually common with them. Most of the above are meant to be read on freestanding candles dressed for hoodoo style workings.