How do you develop ideas for plots?

A note from Nava: In the comments under "Can good work be done in short sessions?" Travelscribble left a question that she hoped a Literary Lady might answer. Perhaps not an exact fit, but Madeleine L'Engle's description of how she developed stories came close, especially since Travelscribble mentioned that she's fond of children's literature and fantasy. I welcome other readers leaving their questions, and I'll do my best to find a fitting answer.

Dear Literary Ladies,
Where do you go looking for plots? Did your stories once begin with just a title in your head? Did you have a mundane thought that you somehow developed into a plot? I enjoy writing and am satisfied with my craft but sometimes feel that I must be really dull or lack imagination. I might add that I am especially fond of children's literature and fantasy. (submitted by Travelscribble)

When I start working on a book, which is usually several years and several books before I start to write it, I am somewhat like a French peasant cook. There are several pots on the back of the stove, and as I go by during the day’s work, I drop a carrot in one, and onion in another . . . When it comes time to prepare the meal, I take the pot which is nearly full and bring it to the front of the stove.

So it is with writing. There are several pots on those back burners. An idea for a scene goes into one, a character into another, a description of a tree in the fog into another. When it comes time to write, I bring forward the pot which has the most in it. The dropping of ideas is sometimes quite conscious; sometimes it happens without my realizing it. I look and something has been added which is just what I need, but I don’t remember when it was added.

When it is time to start work, I look at everything in the pot, sort, arrange, think about character and story line. Most of this part of the work is done consciously, but then there comes a moment of unselfconsciousness, of letting go and serving the work.

— Madeleine L’Engle, Walking on Water: Reflections on Faith and Art, 1980