You can make almost anything in Minecraft, even people. If you want to design a new block-based being while on the go, there's the new Minecraft Skin Studio for Android. This app allows you to build a person pixel by pixel and upload it to your Minecraft game.
Minecraft Skin Studio isn't made by Mojang, the company behind Minecraft, However, it has talked up this app quite a bit, and it seems to be the premiere way to design Minecraft skins. There are already over 500,000 community-created skins available for download.
Note that the skins designed in this app are for use in the desktop version of Minecraft, not Pocket Edition or Xbox. It's $2.99, but that should be of no concern to a dedicated crafter.