there are no actual 'breeds' of rats, just different standards.
Ears come in two types; dumbo (lower set on the head) and standard
Coats come in my varieties; rex (wavy or curly), double rex (also know as patchwork, their hair will grow in once a month then fall out leaving them looking hairless), harley (long coat), silky (a smooth coat with no guard hairs) and standard
Markings are the most numerous, come more common ones are; Self (no white on the body), berkshire, (white belly, paws and tip of tail), and hooded
And eyes; pink (seen on most 'albinos'), ruby (appears black unless hit with a direct light), black and odd-eyed (an eye one color and the other a different color)
I hope this is what you're looking for, if not let me know.
RFTS: you forgot hairless ones. shame on you! sweetipie would be MOST offended!
there's also a couple different sizes. the dwarfs, which come in 2 standards-miniture and normal dwarf-and the standards or "normal sized". think horse sizes. there's the normal sized horse that comes in a range of a sizes just like normal sized rats. then there's the miniture that looks just like a smaller version of the full sized horse which is exactly like the miniture rats. and then there's ponys that are a bit stockier like the normal dwarfs. though the dwarf variety is still fairly rare.
and there's a ton of different colors and patterns. a good place to start looking for pictures of differences here would be he meet my rat section as DonnaK said. but you can also google rat breeders and they'll have different pictures of the different types of rats too.