Well, they are electric. But, I guess I'd never really thought about it. But if you've never wondered what happens if there isn't proper grounding, watch this.
That's Bae Chul-soo, the singer for the legendary Korean band Song Gol Meh. The clip is super old, but was recently unearthed on Japanese site Livedoor News.
The shock burned his hand, but he turned out ok! He's currently a famous radio personality in South Korea. Here, you can hear him interview Noel Gallagher a few years back, and check out this funky Song Gol Meh track "A Chance Encounter" right here.
As tipster Sang points out, there wasn't an ambulance, so they had to pack him up in an auto rickshaw and transport him to a hospital. The announcer said (via Sang), "We are very sorry on this live broadcast. It looks like Mr. Bae has been electrocuted. We are live right now. We are very sorry."
While Yahoo! Answers (heh) says electric guitars are not dangerous, here's an electronics technician saying, "What usually happens is you touch a mike and ZAP, you bounce back, you lose track of the lyrics for a second, but then things are OK, no harm done. But this is dangerous."