They're created when a dielectric — a material that resists the flow of electricity — experiences a catastrophic failure. As such, they're often found in failed insulation when high-voltage equipment kills itself.
Hit any dielectric with a high enough voltage and you can generate one. The most impressive modern artistic examples are the Beam Trees made with a block of acrylic and a linear particle accelerator:
If you are unlucky enough to be struck directly by lightning, you may receive a Lichtenberg figure tattoo, sometimes called a 'Lichtenberg Flower' (Google Image Search at your own risk).
