Transformation Snap is currently limited to Edit Mode.
It is activated through a toggle button in the 3D view header or through the hotkey Shift-Tab.

When activated, an option dropdown appears to let you modify the snapping mode.

When Snap is turned on, enter transform as usual (either with the hotkeys, menus or manipulators), move your mouse near the vertex you'd like to snap to and hold down Ctrl. If you're close enough to a vertex, a small circle will appear around the snapping target and your selection with snap to it.
You can move your mouse around while holding down Ctrl to select different snapping targets. (warning: on heavy meshes, this can get a bit slow)
note: Snapping currently works with Translation and Rotation only
The following paragraphs will demonstrate the different snapping modes.
This first screenshot shows the starting position of the mesh. In this example, the smaller plane will be snapped to the bottom left vertex of the bigger plane.

Using mode Closest, the selected plane snap to its bottom left corner, which was the one closest to the snapping point. This is the default mode and is the one suitable for forst situations.

Using mode Center, the selected plane snaps using the position of the transformation Center. In this case, to better illustrate how it works, center was set to Cursor. Using snap mode Center with center Cursor is the snapping method that offers the greatest flexibility.
note: Does not work with Rotation Snap. In that case, the mode defaults back to Median.

Using mode Median, the selected plane snaps to its middle (where the transformation center would be using Median center). This mode is useful when you want to center part of a model on another.

Snapping also works with transformation constraints.
This example uses Closest snap with a X-axis constraint.
