There's four ways a dog can be white (I think only four):
Dominant white color. I can't think of any examples off the top of my head, except white wolves and foxes. This color is dominant, but contrary to what you'd think, it's very
rare therefore, because you have to breed for it every generation, pretty much (I think only some of the wild greys will express over white). If a dog is solid white and bred to a solid white dog, and sometimes gets solid colored pups in the litter, then that's true dominant white.
Albinism. Very rare, and very unhealthy. If I'm not mistaken it's a recessive mutation. I could be wrong about that.
Hyperextension of white spotting. This is where the white markings on a dog are extended literally all over the body. Often there is ticking or spotting that appears, that indicates the color that is carried on the pigmentation locus (black or liver). Examples, ACD, Dalmations. When these dogs are bred, they produce variations on the spotting - masks, blotches of color, and can even produce very colored dogs with some points of white. The more you breed pattern white to pattern white, on the other hand the further the white spreads, until you start losing pigmentation in key areas such as the inner ear and around the eyes. Hence the deafness issues in ACDs, Dals, and probably JRTs. Any dog with pattern white faces this risk if the white is overdone.
Double merle. Merle is a dominant modifier which is "lethal" when the pups inherit two alleles. Thus, when two merles are bred together, some of the pups will inherit the allele for the merle modifier from
both parents. Inheriting two alleles (homozygous merle) highly increases the risk for unviability, deformity, and stunted cerebral and neural development (including eye and ear problems). These pups are sometimes called "lethal white", but that's a misnomer because they are actually just very pale in pigmentation.
The last three types of white all increase the risk of health problems in dogs, for reasons that are not really well understood at the moment. Pigmentation seems to be linked to in utero development of a great deal of neural tissues, but we don't know much more beyond that.
To Dumdogs: It's easier to think of color when you break it down by locus: There's the main pigmentation which determines whether the base pigment of the dog, as expressed in the nose leather and eye rims, will be black or liver. Black "covers" liver, so when the allele for it is present, it's dominant. There's another locus for yellow, the E locus. When either allele is "turned on", the dog will be some variant of the E yellow. That's yellow like a lab, or a Golden retriever, or the red color of an Irish Setter (Llwellens are bb liver colored).
Then there's the white locus, which is again dominant, the agouti locus, which controls banding on the hair, so that brindles have banding "turned on" and have the brindle modifier, and sables have banding "turned on" and the sable modifier. Finally there's the white spotting locus.
Then there's a ton of modifiers like tri, ticking, brindle, sable, merle, dilution, and many more pattern alleles that shape how all those are expressed. The modifiers act on different loci - merle MM/Mm and dilution dd only act on E and B, while brindle and sable only acts on A (we think). So you could have a sable dog that is merle, but the only place you'd see the merle is where the B/b pigmentation is expressed, and in a sable dog that's only one band of three. This is why sable merle is a very probematic color.
This is a breakdown of the easy colors. Primitive breeds and feral dogs, as well as wolflike dogs such as huskies, make my head explode.
A "silver" lab is bb liver colored, with the recessive dilution allele. Genotype bbdd (remember the liver color is recessive and therefore a liver colored dog is homozygous). A "blue" pitbull would be BBdd or Bbdd - remember B black is dominant and so we wouldn't know whether the dog also carried a liver b allele unless/until the dog produced a liver pup.
Thus, to come back to the original question (was there one? Oh, yes . . .[
]) - it would be quite unwise to breed "for" such a rare color, since both the liver base color and the dilute gene are recessives. The only way to increase the occurence of the combination in the gene pool would be through some really heavy duty inbreeding. Not a good idea, for the sake of mere fancy. I can't think of a faster way to find some really nasty additional recessive mutations and "fix" them in the gene pool. HYPP anyone?
HEre is a web site that is probably the clearest and best-presented discussion of color that I've seen on the web:
http://www.ashgi.org/color/