Mythology - Using Old/Making New

We have previously explored some of my humorous mythology:
{Zoology of Mythical Creatures V.1}
{Zoology of Mythical Creatures V.2}
{Zoology of Mythical Creatures V.3}
But we should also explore the use of mythology in writing.

Mythology is defined as "a body of folklore/myths/legends that a particular culture believes to be true and that often use the supernatural to interpret natural events and to explain the nature of the universe and humanity." (Thank you wikipedia).
Mythology also has been known to spring forth from history, or to replace history entirely. It is quite the sneaky little creature. When an author writes a tome of a novel, much backstory must be given, and often this author will go into the (lengthy 100-1,000 pages of description) mythology of the people whom the story is about.

The question this begets would be: When creating a story, do you create your own mythology, use an old mythology, or a combination of the two?

Many authors use old mythology for their stories. This gives a good background to the lives of characters or explains the attributes and limitations of gods, supernatural beings, and other elements of the story connected to the mythology. This is not to be confused with the use of commonly known fairytales in stories, while fairytales can be part of a mythology, using a fairytale as the base plot of a story (in hopes to give the known tale a new spin) is different than using old mythology. A good example of this kind of using old mythology would be stories or books with Greek gods and more specifically Atlantis in them.

Some authors are creative/smart/dedicated/focused enough to create their own unique (as possible) mythology for their characters. Do I do this? No. Why not? Because I'm lazy, it's good enough just to get a story down, no need to worry about what was before and after that. Will that hurt me in the long run? Maybe, but the more I write, the better my stories get, and with time I'll write mythologies with the best of them (writers). Seriously though, enough about me, if you could take five seconds to stop asking questions and just listen to what I have to say, that would be great. Thanks.
Back to dedicated authors. So a good example of someone who wrote a complete mythology and history for their books would be J.R.R. Tolkien, although I'm sure many fantasy writers have been known to create extensive worlds around their stories. This would be another area in which fantasy authors don't get enough credit. When was the last time James Patterson wrote a complete history and mythology for the fictional characters he made up? How 'bout never. Anyways . . .

When writing or reading fantasy, consider the mythology. If you're reading and they are giving you backstory, you should probably pay attention. If you're writing, consider if it is important to know the mythology of your people and give this mythology the time and energy it needs for it to be as full and interesting as the mythology of our present world.