Good question (both times). I have wondered about this myself, but never bothered to research it. I don't think the answer is common knowledge.

This most commonly used term for this phenomenon is, as you suggested, "washboarding," although in my neck of the woods these nuisances were usually called "chatter bumps." (They're also called "ripples" or "corrugation.")

The principal force forming these regular waves in the road surface is the suspension on our cars. The way cars are built, they "bounce" over bumps in the road, keeping the passenger compartment relatively level and comfortable. When a tire hits an irregularity in the road like a hole, a rock, a branch — even a small one — the car bounces up in the air a bit (the tires do not necessarily leave the road, but they exert less downward force). And what goes up must come down; when the car "lands," it exerts extra pressure on the road surface which forces the gravel or dirt forward and to the sides. This is the beginning of the rut.

Now, you know that when you drop a rubber ball, it doesn't bounce once and then stop. It continues bouncing with smaller and smaller peak heights until it eventually comes to rest. Your car is inclined to do that too, so after crashing down and forming the first rut, the car rebounds up, and crashes down again to form a second smaller rut a short distance ahead, and so on. And since most gravel roads don't have just one irregularity, your car rarely gets a chance to "level out." You'll hit another bump before the previous one tapers down. The end result is that while you're moving forward, the car is also continuously moving up and down. If you tracked its vertical motion, you would see something that looked like a continuous, more or less regular wave (assuming you maintain the same speed). Each "trough" is supplying extra pressure that can create a washboarding rut.

If you're travelling on a flat, new road, this isn't much of a problem. But when you're on a road that already has some minor washboarding, these ruts serve as "cues" to tell your car when and where to bounce. Thus the washboarding has a self-reinforcing effect. The ruts created by the first car will be deepened by the second car. Instead of cancelling each other out, successive cars just make the ruts deeper and deeper.

A lot of this has to do with the road surface; dry gravel roads are the most likely victims, but paved roads and even train tracks exhibit similar (if much smaller) effects.

Source: Alaska Science Forum, University of New Hampshire, The Straight Dope