Fortunately, the Earth does rotate, giving us days every 24 hours. But why does the Earth rotate?
Earth rotates because of leftover momentum from the solar nebula that all of the planets and the Sun formed within. The solar nebula collapsed when a supernova sent a shock through a cold cloud of molecular hydrogen. Each molecule in the cloud had its own momentum, and as they came together, their momentums added up, and needed to be conserved. This set the solar nebula spinning, and created the planetary disk.
As the planetary disk flattened out, each of the planets clustered together from gravity. Over time they accumulated more and more material. And once again, the rotation of the planet was caused by the addition of all the momentum of the particles that came together. This is why all of the planets (except Venus) rotate in the same direction.
It's believed that major collisions early on in the Solar System might have changed the planets' rotation. One collision might have sent Venus spinning in retrograde, and another might have caused the current 23-degree tilt in the Earth's axis.
Because space is a vacuum, there is nothing that will stop the rotation of the Earth or any of the planets. Like spinning tops that don't experience any friction, they'll just keep on spinning forever.