No one has undertaken a large scale study on the coat colour of rodents—possibly because there are more than 1,500 species, of which well over a thousand are rats and mice—but small scale studies of variation within single species have shown that there is a correlation between fur colour and background, at least in those cases investigated.
The similarity seems to be the product of selection by visual predators. Being eaten is a constant danger for these animals, more so than it might be for a dingo or a badger. Any one of those 1,500 rodents is likely to appear on the menu of a bird of prey. Even the giant Gambian rat (Cricetomys gambianus) of sub-Saharan Africa, which is about the size of a cat and able to put up serious resistance with its chisel-like teeth, has to avoid death from above on the points of an eagle's talons.
Matching the background reduces the chance of being spotted by a predator. Individuals that stand out are more likely to be picked off than ones that are difficult to distinguish from their surroundings. In fact, an individual does not have to be particularly noticeable—not decorated in pink and yellow stripes—as long as it is easier to spot than others in the population. The slightest difference in visibility compared to that of other individuals is all that is required to make a corresponding difference in its chances of survival.
Let's look at an example of this. Twenty or so species of pocket mice are found in south-western North America, where they live in scattered brush, grass and rock piles. They are among the smallest of American rodents yet they earn their name not from their size but from the extensible cheek pouches in which they carry food. Most species of pocket mice have grey-brown to sand-coloured fur on the back and sides and pale to white fur on the throat and belly. The pelt colour is usually consistent within a species: all Bailey's pocket mice (Chaetodipus baileyi) are yellow-grey; all Californian pocket mice (C. californicus) are olive-brown; and so on. There is little variation—with one or two noteworthy exceptions.
At eight to ten centimetres long, rock pocket mice (Chaetodipus intermedius) are at the bulky end of the size range for the group. They are found in southern Arizona and New Mexico, where—as their common name indicates—they live among outcrops of rocks. The coat colour of these pocket mice is either pale or dark, depending on the amount of the black pigment (eumelanin) produced by the animal. If the main function of their colour is camouflage, we could predict that pale mice would be found most frequently on pale granite, whereas dark mice would occur in greater numbers on dark lava flows. Those individuals that stand out would be the first to go, leaving the camouflaged ones to breed.
In a study on mouse populations on and near the Pinacate and Pedro Armandaris lava flows, a team of scientists from the University of Arizona found exactly that pattern. Almost 90% of the pocket mice caught on granite had pale fur and up to 100% of those on lava had dark fur. (They used traps so there would be no bias towards either colour.) It was a very strong correlation, as close to perfect as you might expect in biology. Hunting by visual predators obviously had an impact on these populations.
Nachman, M.W., Hoekstra, H.E. and D'Agostino, S.L. (2003). The genetic basis of adaptive melanism in pocket mice. Proceedings of the National Academy of Sciences 100(9): 5268–5273.