Story Layers

Everybody has it: that one book or movie they just keep coming back to over and over, because every time they re-read or re-watch it they catch something they didn't before. It's new every time around.
For me, it's The Count of Monte Cristo. No matter how many times I see it, I'm still riveted every time, and I think part of what makes it so fabulous is the many story layers it has. Every carefully executed plan has a meaningful significance. Every statement or remark is impregnated with underlying meaning. The layers are like pieces of different colored sheer cloth--every time you look at them, you see through certain colors to other colors in a slightly different way.
I try to achieve layering in my own stories, but it can be very difficult. I want my stories to have that read-it-over-and-over-again effect on my readers. I want them to catch things on their fifth read-through that they didn't catch the first four times.
I think a lot of it depends on paying very close attention to the dialogue and action of the characters. Don't have characters do things just off-the-cuff for no reason--or if they do, make it come back and bite them with significance they didn't expect.
Make characters pay attention to what the other characters are doing. This seems to work especially well between villains and protagonists. If, at the beginning of the story, Character A makes a remark to Character B, let B throw it back at A later on. The Count of Monte Cristo is a great example of this in more ways than one.
In his Fiction-Writing Tips, Jeff Gerke touches on this a little bit in his tip on using circularity (tip #40). It's a great tip, definitely worth reading.

What are your thoughts on story layers? Do you use them in your own writing? What book or movie keeps you coming back for more again and again?