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Even in a vacuum, you won't get perpetual motion. Things will lose momentum and eventually stop unless you continue to apply force to keep the thing spinning.
So why does the Earth continue to spin without losing momentum? What "force" is acting on it?
The earth IS slowing down, primarily from the drag of the moon and tides. The easiest (not exactly correct, but conceptually accurate) way to think about this is that the scale is huge and the amounts of energy involved huge. Put a gyroscope in a vacuum and if the bearings are good it will spin for a long time. Increase the mass of the outer ring of it and it will spin even longer. Increase it to the mass of the Earth and...
It got going because it was moving in the first place.
If you go by Big Bang, things were shot out at amazing speeds from a single point somewhere out there. There was a non-uniformity that caused things to clump and whirl together like eddies in a stream of water.
When these slowly spinning eddies contract to form stars and plants, their rotational energy is not dissapated, they spin faster (same energy requires faster spinning when the radius to the center of rotational mass is reduced. An example? Get on a merry-go round with some other kids/people. All of you lean out as far as you can and get someone spinning it. Now all of you pull in, you will go MUCH faster!!!! Just don't be the last one to pull in!!!).
So now everything is spinning. As was said, the earth is slowing down, but VERY slowly. Not much is sloshing around like a raw egg to get it to lose energy into viscous thermal energy, and space has such little mass that there is nothing really pushing on the earth to slow it down.
Increased mass would make it harder to get going...but what caused the spin to begin with? What great force started the mass moving?
By the way, does that mean we're actually going to have shorter and shorter days?
As the Earth slows down, the days become longer, not shorter. But as mentioned, it's a very slow process. Everything in the universe spins. The solar system. Galaxies. Subatomic particles. Everything. We don't know if the universe itself spins, but from our perspective, it probably doesn't matter because we're contained within it, not on the "outside" of it.
How did it all get started in the first place? You have to go back to the beginning of the massive expansion in all directions of the Big Bang itself. As new particles formed, the force of gravity attracted certain particles together. Although some particles would have repelled and push away from each other. Regardless, all this attraction and repelling, in addition to the Big Bang's expansion, would have resulted in more and more motion among particles. Eventually, as particles clumped together, protostars formed. Unstable stars would explode not only creating new elements, but add more motion to the fray.
But why do things spin at all? Look to the formation of planets. The material planets are made of come from such stellar explosions which settles in the form of dust and gas. Massive amounts of particles are blown out in various directions. Particles that become close to other particles can become gravitationally attracted to each other. So, when you have particles (which have a mass) that are set in motion (because of the explosion) and become attracted (because of gravitational attraction), the particles start grouping together. These particles are spinning around each other and form clumps. As more and more clumps of particles do the same, you can end up with larger objects in the accretion disk of dust and debris. Within that disk, much of that dust and gas becomes gravitationally attracted clumping up enough to form new stars and planets.
When a star is formed, its mass is large enough that it's gravity is strong enough to hold or attract a certain amount of the accretion disk together. As the star spins, the disk spins along with it. The debris in the disk continue bumping into each other and become attracted by their own gravity eventually forming planets. The only reason planets don't just turn into stars is because as the debris is swept into the protoplanets, there isn't enough material or strong enough gravity to become massive enough to become a star. Eventually, these protoplanets cool down resulting in the planets we see today in the solar system.
But in the formation process, all the particles are in motion and spinning. You have lots of particles spinning around on their own, and combine with other particles that are also spinning but become gravitationally attracted together to form larger objects. Smaller objects fall in with the spin of the larger objects. When there is less and less material from the accretion disk, the spin begins to slow down. But it's worth mentioning that just because something slows down, doesn't mean it will come to a complete stop. It can't stop because there are too many other things in the galaxy and the universe to keep things moving and happening in one way or another. Everything of mass in the universe are in a constant state of motion.
That's a pretty feeble description but it might give a general idea of what's going on and why the Earth spins.
You could have just said "God Said So" and finished it at that!!!
I know. Shame on me for being one who dares to consider all those silly little details of the processes that happened in between.
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And as far as the origin, man has been debating that for some time. 
I know. Shame on me for being one who dares to consider all those silly little details of the processes that happened in between.
