The vanilla version of Minecraft allows you to venture into the depths of the underworld and the dreaded doomsday kingdom, but not to outer space or other planets. At a certain point, when you touch Minecraft's outer limit, you can't move any further. Many plug-ins on the Internet allow people to change the appearance of the sky. Here's an example of a celestial body that allows you to build on the ancient, dark surface of the moon.

Although you may be on the ground, the sky looks full of stars and black. If you move high enough in the air, you'll look like outer space from some angles, but you probably won't unless you've installed a height modifier.