What Duane said.

The arms of a spiral galaxy don't orbit around the galaxy intact. It's the density waves that we see, and only because that's where the brightest stars live.

Matter on different orbits winds up temorarily creating these denser areas - there was a recent Cassini photo of Saturn's rings showing tight spiral density waves in them, caused by the gravity of one of Saturn's moons - same principle. Except in a galaxy, (if it contains any gas) when an area gets higher density, it becomes a star forming region. And the biggest and brightest stars don't live long, so they never get far from the star forming regions. The stars we can see the farthest are the big, bright, young ones that are found preferrentially near the star forming regions that are found in the denser areas that happen to have a spiral shape.

Rather than like planets orbiting the sun, spiral arms are more like the spiral spokes of one of those pinwheel fireworks. If you took a photo of one it would look like a spiral, and it stays in that form, even though not one single spark in it follows a spiral path - they all move almost straight out from the center.

If the Saturn Ring analogy holds, then the spiral density waves might be caused by a very massive object orbiting our galaxy just outside the rim of the galaxy? Or maybe within the galatic plane itself? Not likely or we would have observed it. Just a thought.