One of the major problems with backlit LCDs is that the backlight must be on all the time -- meaning that a lot of power is wasted as heat from absorbed light, and it's not possible to get a true black on the display.
To solve a different problem (motion portrayal), people have recently suggested using a grid of LEDs as a backlight which are scanned like a CRT beam. This would be useful for moving video, but scanning is irritating for mostly-still images (such as computer screens).
The grid of LEDs could be used in a different way -- as a smart backlight that only generated as much light as was necessary in each bit of the screen, using the LCD elements to add fine detail. Essentially, you'd display a low-resolution black-and-white version of the desired image on the LEDs, and the difference between that and the desired image on the LCD.
This would significantly reduce power usage from the backlight, and would allow dark areas to be truly dark. You would end up with not-quite-dark artefacts in the shape of LED grid cells around single light pixels, though; it might be best to low-pass filter (and then brighten) the backlight image to avoid sharp transitions in the backlight intensity between cells.
Daniel Drucker pointed out that this is remarkably similar to the display being developed for the One Laptop Per Child project, which includes a number of interesting new display technologies.