Drag any window to the left edge of your screen to fill the left half of your screen with the window.
Drag it to the right to fill the right half, and to the top to fill the whole screen with the window.
*NEW*: Drag window to corners to snap window to quardrants. Drag down to snap to bottom half.
Fill Screen Area
While dragging a window, hit any arrow keys and you'll see a shaded area where your window will be resized and repositioned.
Hit the arrow keys again to see what other options you have for an edge. For example, after you've hit the arrow keys once and a shaded area appears, hit the left arrow button to see what other options you have for the left edge of the window you're about to resize. Hit the right arrow button to do the same for the right edge and so on.
The snapping options that are available depend on whether there's another window's edge next to your cursor (when dragging a window).
Works with multiple monitors
Alternatives to arrow keys: W (up), S (down), A (left) and D (right)
Windows now snap to quarters of screen. Just drag windows to any corner. Bottom half of screen also supported
Alternative hotkeys as requested. W (up), S (down), A (left) and D (right)