As well as my Van de Graaff generator, I experimented with high voltage in another project. However, this one was much more dangerous and from a kit. Still, it was fun.
Here's my short write-up from my old site, with a couple of minor edits.
This is a Jacob's Ladder I built from a kit from amazing1.com. Unfortunately, the kit had some problems in it. I had a lot of help from my parents and a couple of their friends, and we got it working eventually.
A Jacob's Ladder is basically two metal prongs (shown in image above), with a high voltage difference between them. The difference is large enough to jump across the air at the base, where the metal prongs are very close together (but not touching). The arc (seen in image on left) is plasma, and much more conductive than air. This acts as a contact between the prongs, allowing electrons to travel from one to the other much more easily than through air. The arc heats up the air around it, causing it to drift up (and helped along by a small fan at the base). When the arc gets long enough, it becomes easier for the electrons to jump across the air at the base again. When this happens, the top arc breaks and a new arc forms at the base.