evolution - Can species back-evolve?

Just to clarify, as one might read your question as if humans had evolved from dogs - humans and dogs have a common ancestor, one is not a direct descendant of the other.

In terms of evolution running backwards, it has actually been experimentally tested in microorganisms, where you can check the phenotype (characteristics) of an organism over hundreds and thousands of generations. One example that comes to mind is Joe Thornton's research where he reconstructed a gene for an ancient protein and compared it to the more modern versions. They found out that the key mutations that modified the protein sequence could not be simply changed back to obtain the more ancient form, because in the meantime many neutral mutations had accumulated in that protein and while they did not change the protein sequence, they interacted with the protein-changing mutations and prevented the de-evolution of the protein.

The paper I have in mind (there are many more on this) is: Bridgham, Jamie T, Eric A Ortlund, and Joseph W Thornton. 2009. “An Epistatic Ratchet Constrains the Direction of Glucocorticoid Receptor Evolution.” Nature 461 (7263) (September 24): 515–519. doi:10.1038/nature08249.

On the other hand, in a sort of more esoteric example (as it is not directly de-evolution), blind cavefish have multiple mutations (and sometimes in multiple genes) that cumulatively result in loss of vision. Let's then say you have population of the fish that have sight-losing mutations in gene A and another population with mutations in gene B. Both populations are blind, but if you could cross the fish from the two populations, the eye-loss mutations in genes A and B would be substituted by 'correct' versions from the other population and thus both fish would be able to see again. While not de-evolution in itself, it shows that for relatively simple changes that were not influenced by other changes in the genome, you can rewind the clock and get the long-lost phenotypes, even like the sight.

See here: Borowsky, Richard. 2008. “Restoring Sight in Blind Cavefish.” Current Biology : CB 18 (1) (January 8): R23–4. doi:10.1016/j.cub.2007.11.023. (this is a description of the research, not the actual paper; but it links to it).

Both these examples are super-cool (IMHO), and in my collection of all-time favorite evolutionary stories. But practically speaking, what you're asking for (from humans and dogs to their most common ancestor) is not possible. Too many variables (both genetic and environmental and stochastic) to control. The papers are behind the paywall, but if you want them, send me an email.