Most products generally require advertisements of some sort to garner any sort of attention and purchase from consumers. So when you get something like Minecraft which has sold over a million units via word of mouth that's quite an impressive feat.
That hasn't stopped fans from making their own videos attempting to describe the game and experience however.
This trailer does a fairly good job, I don't care for the Inception music however:
This ad looks a bit more professional even if it makes no sense:
And I'll be honest, Minecraft is one of those games you have to experience yourself to understand why it's so popular. Maybe that's why there are no official ads currently. If all you've played is the free version then I can see why you'd be bored or uninterested. I'd recommend shelling out the $15-$20 for the full version and see what you think. If you're anything like me, you'll be up till 5AM each morning for a week.