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"The American Bobtail Breed"
from Wikipedia.com
Contrary to its rugged appearance, the American Bobtail is not a "wild" cat, but descends from naturally occurring bobtailed cats "found in the wild". 
  (Excerpt from http://cats.about.com/cs/breedprofiles/p/americanbob.htm)
Enjoy the Links below to many differing views of the American Bobtails recent origin...and history...
 one thing they all have in common...
A naturally occuring bobbed tail that 
is genetically dominant.
And that "wild colors" are currently preferred, 
But they come in all colors!
Points are not a natural occurance, but occur from siamese or himilayan crosses.
The more you know about the breed the better able you are to determine if this is a good fit for you!
TICA recognized the breed as a naturally occurring cat breed in 1989. Feral bobtailed cats were the foundation stock of this breed, but most breeders do not use feral cats anymore. 
Excerpt from http://www.cat-breed-info.com/american-bobtail.html
The Natural American Bobtail is an active cat.  It will play with toys. My cats will even play fetch!  My Jazzmyn will bring me a paper ball and meow for me to toss it for her.  They have very dog-like Purrsonalities. In addition to high energy levels, the Bobtail is also very friendly and extremely intelligent. The Bobtail is able to bond well with strangers and does well with children and they do not mind being handled.
Several of our kittens have been leash trained and follow like puppies.
 American Bobtails come in all colors and patterns, however since breeding to other recognized breeds are not allowed, "points" would not normally appear.
Excerpt from http://www.catsunited.com/html/american_bobtail.html

The gene that is responsible for long hair in cats is recessive, meaning that two copies of the gene would be needed to produce long hair. In other words, both parents would have to have the long hair gene. A cat with only one copy of the gene would be short-haired. 
Excerpt from http://www.cat-breed-info.com/long-hair-cat-breeds.html
Tabby-types
Credit to MessyBeast.com for this photo
"A Tabby Cat has a very identifiable coat consisting of stripes, dots or swirl-like patterns.  A common misconception of the Tabby Cat is that people believe they are an actual breed of cat.  Well my friends, I am here to tell you that the Tabby is not a breed of cat as this “tabby” pattern can be found in a variety of cat species.  This tabby pattern is a naturally occurring feature that is believed to be related to the domestic cat’s wild ancestor, the African Wildcat."  
Credit for this excerpt goes to 
http://www.wild-facts.com/category/mammals/tabby-cat/