I think this picture is worth a thousand words, particular in ref to Raoul's post below. It shows how randomly oriented elliptical stellar orbits, through gravitational coupling, can result in spiral structure. Actually, the stars are distibuted pretty uniformly throughout the disk, density being strictly a function of distance from the galactic center, so there are as many stars in a spiral arm as there are between them. But as the arm (density wave) passes through a molecular cloud in the disk, it can precipitate star formation, and the very bright but short-lived massive supergiants formed act as a marker for the arm. As the arm moves on, the bright "marker" stars burn out or supernova themselves to pieces behind the arm, while new ones form up ahead as the wave proceeds to race around the disk.

Of course, this diagram represents an ideal case. In real galaxies, you have spiral arms in a variety of states of definition; old, deteriorating arms, remnants of earlier arms, breaks, spurs, gaps, etc. Astronomers have traditionally called this type of galaxy a Grand Design Spiral, a phrase that always sent chills up my spine. It just goes to show you that if you pile enough matter in one place and add in a whole lot of energy, it can behave in beautiful and unexpected ways.