Yea, try a search. As you will find there is way too much variation to cover it in a forum post.
Just off the top of my head -
Domestic rats:
Ear types: standard (top-ear) and dumbo. Dumbo is a simple recessive
coat types: standard, rex, hairless. There are allegedly 3 different hairless genes, each one with various health issues. All are simple recessives. Rex is co dominant. Double rex or homozygous rex will look almost hairless, or will have patchy coat, and or will lose hair and grow it back in cycles. Rex looks like a curly coat.
colors:
Too many to list, I currently have blues, buffs, blue-buffs (platinum), blacks. All are simple recessives.
Patterns/Markings:
Most common is the hooded/berkshire/self gene. Homozygous is hooded, heterozygous is berkshire. wild type is "self" or solid colored. I have never seen or produced a self, though breeding 2 berkshires should produce 1/4 selfs, I've never had it occur. Currently my rats are about half hooded, half berkshires (solid with white paws and white patch on belly)
There are also siamese, himalayan, masked, capped, blaze (white stripe on face), and many others.
African soft furred rats:
Distinct species of rat, not to be bred or intermingled with regular domestic rats. Much smaller than domestic rats, almost no smell. Good feeder for smaller snakes like BPs and corn snakes as they never get too big for them to eat.
Much simpler color and pattern varieties, and since no more can be imported in the US we are pretty much stuck with whatever strains are in the country.
patterns: one gene that is known, works the same as hooded/berkshire/self gene in domestic rats. Homozygous is "pied", white head and rear section with colored back and sometimes spots on rear. Heterozygous is "masked" or "head stripe" type. Mostly solid with white stripe(s) in head and I believe white belly. wild type is solid colored.
Colors - There are 2 colors with 2 more caused by combining them with a red eye dilute gene.
Agouti (black) and Cinnamon(brown-grey). Add to these colors the red eye dilute gene and you will get 2 shades of tan. AFAIK there is no true albino gene known but many people call the red eye dilutes "albinos", though technically they are not.
Domestic Mice:
I don't know much about mouse genetics. In the past I've had albinos, reds ( fawn), brindles, greya, agoutis.
Certain genes have health issues associated with them. Like it is never good to breed 2 reds or fawns together, as the homozygous form of the fawn gene is lethal and they will die in the womb. Every spotted mouse I have produced has died early before breeding. Same with any I have bought at Petco.