How to create a drop shadow only on one side of an element?

Just use the spread parameter to make the shadow smaller:

.shadow {
  -webkit-box-shadow: 0 6px 4px -4px black;
  -moz-box-shadow: 0 6px 4px -4px black;
  box-shadow: 0 6px 4px -4px black;
}

<div class="shadow">Some content</div>

Live demo: http://dabblet.com/gist/a8f8ba527f5cff607327

To not see any shadow on the sides, the (absolute value of the) spread radius (4th parameter) needs to be the same as the blur radius (3rd parameter).

If you have a fixed color on the background, you can hide the side-shadow effect with two masking shadows having the same color of the background and blur = 0, example:

box-shadow: 
    -6px 0 white,         /*Left masking shadow*/
    6px 0 white,          /*Right masking shadow*/
    0 7px 4px -3px black; /*The real (slim) shadow*/

Note that the black shadow must be the last, and has a negative spread (-3px) in order to prevent it from extendig beyond the corners.

Here the fiddle (change the color of the masking shadows to see how it really works).

div{
    width: 100px;
    height: 100px;
    border: 1px solid pink;
    box-shadow: -6px 0 white, 6px 0 white, 0 7px 5px -2px black;
}

<div></div>

UPDATE 4

Same as update 3 but with modern css (=fewer rules) so that no special positioning on the pseudo element is required.

#box {
    background-color: #3D6AA2;
    width: 160px;
    height: 90px;
    position: absolute;
    top: calc(10% - 10px);
    left: calc(50% - 80px);
}

.box-shadow:after {
    content:"";
    position:absolute;
    width:100%;
    bottom:1px;
    z-index:-1;
    transform:scale(.9);
    box-shadow: 0px 0px 8px 2px #000000;
}

<div id="box" class="box-shadow"></div>

UPDATE 3

All my previous answers have been using extra markup to get create this effect, which is not necessarily needed. I think this is a much cleaner solution... the only trick is playing around with the values to get the right positioning of the shadow as well as the right strength/opacity of the shadow. Here's a new fiddle, using pseudo-elements:

http://jsfiddle.net/UnsungHero97/ARRRZ/2/

HTML

<div id="box" class="box-shadow"></div>

CSS

#box {
    background-color: #3D6AA2;
    width: 160px;
    height: 90px;
    margin-top: -45px;
    margin-left: -80px;
    position: absolute;
    top: 50%;
    left: 50%;
}

.box-shadow:after {
    content: "";
    width: 150px;
    height: 1px;
    margin-top: 88px;
    margin-left: -75px;
    display: block;
    position: absolute;
    left: 50%;
    z-index: -1;
    -webkit-box-shadow: 0px 0px 8px 2px #000000;
       -moz-box-shadow: 0px 0px 8px 2px #000000;
            box-shadow: 0px 0px 8px 2px #000000;
}

UPDATE 2

Apparently, you can do this with just an extra parameter to the box-shadow CSS as everyone else just pointed out. Here's the demo:

http://jsfiddle.net/K88H9/821/

CSS

-webkit-box-shadow: 0 4px 4px -2px #000000;
   -moz-box-shadow: 0 4px 4px -2px #000000;
        box-shadow: 0 4px 4px -2px #000000;

This would be a better solution. The extra parameter that is added is described as:

The fourth length is a spread distance. Positive values cause the shadow shape to expand in all directions by the specified radius. Negative values cause the shadow shape to contract.

UPDATE

Check out the demo at jsFiddle: http://jsfiddle.net/K88H9/4/

What I did was to create a "shadow element" that would hide behind the actual element that you would want to have a shadow. I made the width of the "shadow element" to be exactly less wide than the actual element by 2 times the shadow you specify; then I aligned it properly.

HTML

<div id="wrapper">
    <div id="element"></div>
    <div id="shadow"></div>
</div>

CSS

#wrapper {
    width: 84px;
    position: relative;
}
#element {
    background-color: #3D668F;
    height: 54px;
    width: 100%;
    position: relative;
    z-index: 10;
}
#shadow {
    background-color: #3D668F;
    height: 8px;
    width: 80px;
    margin-left: -40px;
    position: absolute;
    bottom: 0px;
    left: 50%;
    z-index: 5;
    -webkit-box-shadow: 0px 2px 4px #000000;
       -moz-box-shadow: 0px 2px 4px #000000;
            box-shadow: 0px 2px 4px #000000;
}

Original Answer

Yes, you can do this with the same syntax you have provided. The first value controls the horizontal positioning and the second value controls the vertical positioning. So just set the first value to 0px and the second to whatever offset you'd like as follows:

-webkit-box-shadow: 0px 5px #000000;
   -moz-box-shadow: 0px 5px #000000;
        box-shadow: 0px 5px #000000;

For more info on box shadows, check out these:

• http://www.css3.info/preview/box-shadow/
• https://developer.mozilla.org/en/css/-moz-box-shadow#Browser_compatibility
• http://www.w3.org/TR/css3-background/#the-box-shadow

I hope this helps.