You are allowed to create videos of Mojang games, upload or stream from YouTube or other video sites, and monetize those videos. It's free advertising for us, and we like watching you play our games! Visit account.mojang.com/documents/brand_guidelines for the most up-to-date language on monetization, and account.mojang.com/documents/minecraft_eula for additional information.
Music in Mojang Games
You are allowed to have the music from Mojang games playing within a monetized video showing the gameplay of Mojang games. The usage of that music outside of normal gameplay may be restricted (see below). Here are the artist's policies on the use of their music:
Minecraft music - C418's music policy