A lone flame against a dark backdrop makes a great scene, but, on most automatic cameras, a washed-out or drab picture. Digital Photography School has sound advice on capturing fire in a frame. For instance, if you're practicing or shooting with a candle flame, don't focus on the flame itself, but on the end of the wick:
The flame itself will not be in super-clear focus as it is producing the light while being a three dimensional object, meaning the intensity and points to focus on it will be varied. If your camera has spot metering, use it and take a reading off the flame itself. This may produce a fairly dark image, so experiment with overexposing a little by slowing down the shutter speed.
Many of the principles of shooting fireworks apply, but DPS' post goes into detail about getting tricky/nifty shots, like the fire trail pictured above. Drop links to your own successful flame shots in the comments below. Photo by Gaetan Lee.