Twitch Plays Pokemon started this trend. Twitch ended up taking down the stream for a while, which caused a massive uproar because TPP exploded in popularity and was the #1 most-watched stream at the time. I think they took it down because the chat volume was borking their servers. It was against their policy for a while, not sure if it still is.

I remember thinking it was dumb, and then inexplicably getting hooked to it and keeping it on a second monitor all day at work. Fun times.