Why is everything spinning? Moons, planets and stars all rotate on their axes, moons orbit planets, planets orbit stars, spiral galaxies rotate around super-massive black holes, etc. What force is causing all this spinning?

Conservation of angular momentum

Explanation:

When the objects spread in universe after big bang, because of the tremendous force, they gained angular momentum and started to rotate. Since, then the object continue to rotate on their axis because of conservation of angular momentum. In vacuum of space there no other forces that can stop these rotation, therefore, they continue to rotate.