This Edward Muybridge sequence is excellent for showing a typical dog run cycle. A dog's run, like most animals, is notable for two things: (1) the very long period of suspension, where all legs are off the ground and (2) the compression and expansion of the spine.
In a dog's run, the head generally leads, and in many ways, the feel of the run is that the head is pulling the entire rest of the body forward. Notice, for example, in the image above, how the neck between the first frame and the second goes from compressed to extended. It remains extended until the next to last frame of the cycle. The shoulders follow suit, extending fully by the third frame (notice how straight the back is at that point), and the hips follow about one frame later.
The spine is fully compressed on the last frame of the row (6) and full extended on the third. When compressed, the head to the spine forms a beautiful S-curve, and when extended, it forms a very shallow, almost linear reverse-S curve. It's this reversal of curves that gives the the run energy.
The hips are at their highest point on the next-to-last frame (immediately before the compression). They are at their lowest on the second frame. The shoulders are almost the opposite, at their highest on the third frame and their lowest on the fifth (when the hips are at their highest).
Now, to the legs. In a run, the front and rear legs work in slightly offset pairs, more similar to a bound, like a squirrel: