Some of these cat breeds are:

Mackerel tabby cat, showing the characteristic "M" on its forehead.

Tabby cat 
Striped, with a variety of patterns. The classic "blotched" tabby (or "marbled") pattern is the most common and consists of butterflies and bullseyes. The "mackerel" or "striped" tabby is a series of vertical stripes down the cat's side (resembling the fish). This pattern broken into spots is referred to as a "spotted" tabby. Finally, the tabby markings may look like a series of ticks on the fur, thus the "ticked" tabby, which is almost exclusively associated with the Abyssinian breed of cats.

Female tortoiseshell-and-white cat.
Tortoiseshell and Calico
This cat is also known as a Calimanco cat or Clouded Tiger cat, and by the nickname "tortie." In the cat fancy, a tortoiseshell cat is randomly patched over with red (or its dilute form, cream) and black (or its dilute blue) mottled throughout the coat. Additionally, the cat may have white spots in its fur, which make it a "tortoiseshell and white" cat or, if there is a significant amount of white in the fur and the red and black colors form a patchwork rather than a mottled aspect, the cat will be called a "calico." All calicos are tortoiseshell (as they carry both black and red), but not all tortoiseshells are calicos (which requires a significant amount of white in the fur and patching rather than mottling of the colors). The calico is also sometimes called a "tricolor cat."

Siamese cat, classical colorpoint pattern.

The colorpoint pattern is most commonly associated with Siamese cats, but may also appear in any domesticated cat. A colorpointed cat has dark colors on the face, ears, feet, and tail, with a lighter version of the same color on the rest of the body, and possibly some white.