I'll look for pics later, but here are most of the common ones:
Red, yellow/gold, orange - self explanatory. Orange is often referred to as red for some reason, but true reds are a real, deep red. Pink and cream platys also crop up occasionally.
Sunset - Yellow body deepening to red on the caudal peduncle, running through shades of orange on the lower part of the body, very attractive.
Coral - blueish body with a big orange/red blotch taking up the whole caudal peduncle.
Washed out coral - Whitish body with pinkish markings as above.
Blue - this is an interesting spotted pattern, the blue platy is not a solid colour.
Black - Interestingly, an essentially white fish with black iridescent scales. A modi of the tuxedo strain, using a transparent (cellophane fin) base colour and extending the pattern over the head and belly.
Comet - Usually has a pale yellow body, but occasionally this marking is combined with another colour pattern like tuxedo. The 'comet' bit refers to two black streaks on the tail, one on the topmost few rays and one on the bottom most few.
Partial tuxedo - Red/yellow/orange platy (very occasionally white or blue) with a broad black (often with iridescence) stripe on both sides.
Full tuxedo - Red/yellow/orange head and belly, with a touch of the base colour in the fins. The rest of the fish is iridescent black.
Wagtail - A (usually) red/yellow/orange/sunset platy with black fins.
Dalmatian - Red/yellow/orange/sunset with black spots of varying size and thickness.
Piebald - Random patches of colour (usually black/greenish iridescent) over any of the normal base colours.
Mickey Mouse - A blotch on each side of the caudal peduncle that looks like a Mickey Mouse head with ears. Extremely dominant marking that throws back constantly, the nemesis of breeders. Often turns up in random genetic mixes, so may appear on the oddest of colours.
Bleeding heart - white base colour with vertical bands of red on most of the body, often darker and closer together on the caudal peduncle. Often accompanied by black spotting or streaking. In its true form a very attractive colour form, but rarely seen in pure form as it is recessive, difficult to induce to breed true, and good bleeding-heart lines are still rare and expensive.
Variatus wild - I mention this because it's cropping up everywhere lately. Blue platy (the spotted blue pattern I mentioned) with bright red fins. Usually on an obviously variatus-based fish.