The Writing Muse

Ah, the muse. The thing which causes brilliant ideas to appear in your head, which you are then inspired to turn into reality. These strokes of inspiration can be caused by many things. Let's delve into the sources of the muse, shall we?

God

Sometimes, things in your writing work out so well, it's like the divine hand of providence. Maybe the story goes in a different direction than you intended, but it vastly improves the plot. Maybe an idea ties things together perfectly. Either way, it seems too great to be mere happenstance.

Excitable Nerdy Fangirl/boy

OH, THIS IS SO COOL!!! I totally need this for my world-building/character-naming/etc. plans. And I'm not just saying that because I'm totally obsessed with this.

Here's a bunch of interesting things from other languages. I can totally use some of these, they're perfect. Hey, what if I made a phrase that's a reference to this real-life Celtic legend?

This is a fascinating concept, I'm going to make a million of my characters this way. And this weird obscure fact is awesome. I wonder how a similar gene would manifest in dragons. I'll have to consider their wings, and whether they're fire-breathing or not, and...

Characters

Sometimes a very stubborn muse, and won't take no for an answer, characters have a way of demanding what they want. In some cases, they can defy you, outsmart you, pretend not to hear a word you say, and deviate from the plan without warning.
For example, when you jokingly say, "Wouldn't this be fitting as the emblem for your kingdom?" Closely followed by, "No, another kingdom already has a similar emblem! I was kidding!" But no matter how many reasons you give, they don't listen, and then use the classic excuse of "But this is ours. Why shouldn't we have it?"

And we won't discuss the neighboring kingdom's emblem. If anyone asks, it was unintentional. Coincidence. And your characters outsmarted you.

Or when you plan for your characters to have a meeting in which they get things accomplished, in regards to negotiations with a kingdom. Instead, they get into an argument, and storm off in a huff. But in the events that follow, two of the characters, who usually don't get along, have a conversation in which they finally begin to see the other as they really are. They understand each other more, and various conversations with other characters get them to see some sense. So despite the disastrous meeting, they accomplished a fair bit.
So as you can see, the whole characters-taking-over thing can go either way. It could result in arguments with them (no guarantee you'll win), or with things turning out better than what you'd planned.

...Apparently I Need This

There's a scene in the Disney film 'Ratatouille', in which Remy is leading Linguini by the hair and having him grab ingredients to prepare a dish. Linguini is stammering and apologizing as he's forced to fly around the kitchen and steal things from everyone's stations. "Sorry, excuse me. Apparently I need this."

And honestly, sometimes that's how it works. Someone or something is insisting that you need this. You can't explain why, it's just where the muse is taking you. See the above entries for possible origins of this feeling.

Miscellaneous

Occasionally, you come across something that makes you think, "That would be great in a story!" Perhaps a song inspires you, or a piece of mythology, or a funny anecdote about your aunt. Maybe it's that weird news story you saw online last week. Even the most random things can suddenly become a terrific story element.

Or perhaps you're working on something, and think, "You know, this would tie in well with..." Suddenly, an object owned by a minor character, originally a trivial thing only appearing in a single chapter, turns into an important plot point years later in the timeline.

Writing inspiration comes in many forms, from many different places. So what interesting things has your own muse resulted in? Let me know in the comments.