This is an updated repost; the original version was posted December 19, 2010. I have added photos and changed several of the links.
Two dilution genes are so rare that their effect on all base colors is not even well understood.
Mushroom has been found in only a few breeds: Shetland Pony, Haflinger and possibly the American Quarter horse. At first glance, it looks like silver dapple acting on a black background. The body color is a flat beige or sepia, and the mane and tail are lighter than the body. But mushroom horses, unlike silver dapple, are very rarely dappled. Further, their eyelashes normally remain dark.
DNA tests show conclusively that these horses do not carry silver. Even more surprising, gene tests indicate the underlying color is not black, but chestnut.
Mushroom has been shown to be due to a recessive gene, tentatively identified as the mushroom allele at the mushroom locus. The effect on base colors other than chestnut is at the present time unknown.
It is difficult to know how common the mushroom allele is, partly because most mushroom horses are misidentified as silver dapples.
The other rare dilution as been found in two closely related Arabian horses. Their pedigrees suggest a recessive gene, and their appearance suggest that the effect of the double recessive is similar to that of a single champagne gene, though there is less effect on red pigment or skin color. Eye color is lighter than normal. However, this is based on only two horses.
A single horse can have any two alleles at each locus, but there are six different loci that have at least one allele that causes dilution. Thus a horse can easily be a palomino and a dun (linebacked palomino) or a dun and a silver dapple on a black background (silver grullo.) Telling which genes are actually present based on the appearance of the horse, however, can be a major problem without DNA testing. In many cases, a horse with multiple dilution genes will just look cream, or even white. I mentioned this before, when I posted a photo of a horse the owner thought was palomino and I thought was buckskin silver dapple. Here’s another photo of the same horse.
We can summarize the loci and the alleles we have discussed previously, with links to the previous posts, as follows:

Liver chestnut (note the lightening toward the hooves), bay, and red chestnut.The one almost hidden is palomino.
Agouti locus: This has been shown to be the agouti signalling protein (ASIP) locus. The exact number of alleles is uncertain, but probably include wild-type bay (some red on lower legs), bay, seal brown (black with some red shading) and non-agouti (black.) More red is dominant to more black in this series. Most blacks, and particularly most intense blacks, are due to non-agouti.
Extension locus: This has been shown to be the melanocortin one receptor (MS1R) locus. There are three alleles. The most dominant first, they are dominant black, wild-type, and recessive red (chestnut). This locus determines whether black pigment can be produced. Two copies of the recessive red allele or one of the dominant black allele completely hide whatever is present at the agouti locus. Dominant black is relatively rare and still subject to some controversy.
Because agouti and extension interact, I covered both in separate posts, here and here. Because these base colors can be modified, I also described the classes of modifying genes.
Cream locus: This has been shown to be the membrane-associated transport protein (MATP) locus. The alleles are (in order of dominance) cream, wild-type, and pearl. Red pigment is affected far more than black, especially if the horse has one wild-type gene. Palomino, buckskin and smoky black are the result of a single cream allele with the other being wild-type. Two cream alleles give cremillo, perlino, or smoky cream, which cannot always be told apart. The pearl allele is a relatively recent discovery, but it appears to be at the cream locus.

Red Dun
Dun locus: As of 2009 the locus had not been found, so no direct DNA test was available. There is, however, a test for a linked gene. The alleles are dun (wild-type) which is dominant to non-dun. Both red and black pigment are affected, and in addition dun produces a dorsal stripe and other variable striping effects. There is a dun, specifically a grulla, in my novel, Tourist Trap.
Champagne locus: This has been reported to be a mutation in Exon 2 of SLC36A1, and a gene test is available. The alleles are Champagne (dominant) and wild-type, and it does not matter whether one or two doses of Champagne are present. The effect is to dilute both red and black, but a single dose of champagne causes more dilution of black on the body than does a single dose of cream. Eye and skin color are also affected.
Silver Dapple locus: This has been shown to be the pre-melanosomal protein 17 (PMEL17) locus. The alleles are silver (dominant) and wild-type. This gene dilutes black to a variable extent, but has little or no effect on red, and appears to dilute the coarsest hairs most strongly. Like champagne, it is a simple dominant.
There are three more groups of loci which produce white areas or hairs on the horse: those that produce white markings on head and legs only, those that produce interspersed white hair, and those that produce white areas on the body. I’ll repost these with updated pictures later, but you can find the original posts by using the index.