All things attract or repel each other, likewise all things have an initial speed in a specific direction. As they move, any object will be attracted to another object and so begin to orbit the other object. This causes the apparent 'spin'.

An example is that you are rotating around the earth, which is rotating around the sun, which is rotating around another sun, which is rotating around the galaxy, which is rotating around a cluster, which is (possibly) rotating around the universe.

  Such a process is unstoppable once it has begun as each object will cause another object to move and result in a spin. The only way for things to not result in 'spins' was for a stagnant, non-chaotic universe. This would be a dead universe as there would be no interaction between particles.