Hi ranrod,
Great questions. Let's start with our solar system. Think of it when it was in its infancy as just a collapsing cloud of gas, before the sun and planets had congealed. Virtually all astronomical things are noticeably spinning in some direction, and our infant cloud of gas is no different. As the cloud collapses the gas spins faster and faster (just as the ice skater spins faster when his arms are pulled in). Now the part of the cloud that is spinning the fastest starts dominating. In other words, the particles whose orbits don't align with the "spinning" plane collide with the particles that are in the "spinning" plane, and eventually virtually all the particles collapse into a spinning disc like structure. Then the planets form from the gas that is in this same plane. And sure enough, that's what our solar system looks like. This so called "nebular hypothesis" was put forth way back in the day (early 19th century) by Laplace and has since received observational validation.
Galaxies are supposedly assembled in the same way. Except instead of a sun and planets congealing, it's stars that congeal from the gas.
-bombadil