Aligning an object to the grid

I need to align various objects precisely to the Grid as I construct a model. Currently the alignment point is in the centre of a cube, so it sits IN the grid instead of ON the grid. How do I easily change this so that the cube aligns to the grid so that the bottom surface is precisely flush with the grid?

One way to do it would be to change your object origin ( the little dot in the middle of your object ) , by going into edit mode >> select all >> grab >> move mesh so that the bottom face is aligned with the object origin.
There might be an easier way, but blender isn’t exactly a cad program. You may want to check the blender wiki on snapping functions though, just to be sure.
http://wiki.blender.org/index.php/Doc:2.6/Manual/3D_interaction/Transform_Control/Snap_to_Mesh

To further support Modron’s suggestion - in edit mode select one corner vertice, Shift-s Cursor To Selected, back to Object mode on T-panel button Origin - to 3d Cursor. Now mouse left click near some Grid point, Shift-S Cursor to Grid and Shift-s Selection to 3d Cursor.
That will put corner of your object (and the bottom part, if it’s not rotated) exactly on the Grid.
However, since grid is just a convenience, you could set Snap to Grid (it is set so by default) and use Ctrl Grab to move object by grid increments.
To have a neat view, default cube added at coordinate center needs to be ctrl grabbed z one unit.

Great suggestions - thanks, it worked for me!