Jacob's Ladders (JLs) look really cool, and can be made out of many power sources. The best easily available transformer is a NST (neon sign transformer) but OBITs (oil burner ignition transformer) and IC's (ignition coil from a car) work OK too. Believe it or not, a dual IC system can outperform a OBIT. Remember that all of these power sources are potentially lethal! The NST is the one to really watch out for. Safe operation should incorporate a momentary or "deadman" switch.
The picture below shows a OBIT powered JL. The rods are simply pieces of wire. If you look closely, you will notice that the rods are not quite centered between the terminals of the transformer because one rod has a longer "leg". This arrangement makes it easy to adjust the arc start point distance. This unit can be run for long periods, I have run it for an hour at a time.
The JL shown below is powered by a 15kV, 120mA NST. The rods are 3/16" brass, around 14 inches long, and they are set a 5 degree angle, about 1/2" apart. The base is acrylic. This unit will not withstand continuous operation, as it gets quite hot and would melt the base. I limit runs to a few minutes, and the rods get sizzling hot.
Why does it work? The rods of the ladder are set close enough together that the transformer can easily jump the gap. When the arc jumps across, it creates heated ionized air. Ionized air is a good conductor, and since the ionized air is hot, it rises. As it rises, the arc follows the ionized air because it is the path of least resistance. This allows the arc to spread much wider than the voltage of the transformer would normally allow.