Minecraft is a game developed by Mojang, and you can read all about it on the Minecraft Wiki. Many of the people here at Vivian Video really like it, and several nifty projects have come about because of it.
For one thing, it may possibly be covered by the Let's Play Awesome team someday, covering play sessions of whatever activity we feel like. There wouldn't technically be any order, or end. That's sort of how Minecraft goes, though.
There's also RP City, which is a map started by Brandon Vivian but contributed to by many other people, not all of them affiliated with Vivian Video. It's comprised of many other maps as well, and is divided up into cities. You can read more about it on it's main article.
Minepedia, a very poorly run wiki about Minecraft that is scarcely moderated, can be a good place for a quick laugh. Hitting the random button can produce some pretty funny results, and some of those are documented via screenshot on this album here.
Brandon has been playing since version Alpha 1.0.3, and shortly thereafter spread it to most of his friends. Thomas Quigley wins, though, having been around since sometime before Survival Test was even released. He used to play zombie survival on classic mode. He was the one who introduced it to Brandon.