Another way (not mentioned here yet) is with Flexbox.
Just add the following code to the container element:
display: flex;
justify-content: center; /* Align horizontal */
align-items: center; /* Align vertical */
.box {
  height: 150px;
  width: 400px;
  background: #000;
  font-size: 24px;
  font-style: oblique;
  color: #FFF;
  text-align: center;
  padding: 0 20px;
  margin: 20px;
  display: flex;
  justify-content: center;
  /* align horizontal */
  align-items: center;
  /* align vertical */
}
<div class="box">
  Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh
</div>
 
 
Alternatively, instead of aligning the content via the container, flexbox can also center a flex item with an auto margin when there is only one flex-item in the flex container (like the example given in the question above).
So to center the flex item both horizontally and vertically just set it with margin:auto
.box {
  height: 150px;
  width: 400px;
  background: #000;
  font-size: 24px;
  font-style: oblique;
  color: #FFF;
  text-align: center;
  padding: 0 20px;
  margin: 20px;
  display: flex;
}
.box span {
  margin: auto;
}
<div class="box">
  <span>margin:auto on a flex item centers it both horizontally and vertically</span> 
</div>
 
 
NB: All the above applies to centering items while laying them out in horizontal rows. This is also the default behavior, because by default the value for flex-direction is row. If, however flex-items need to be laid out in vertical columns, then flex-direction: column should be set on the container to set the main-axis as column and additionally the justify-content and align-items properties now work the other way around with justify-content: center centering vertically and  align-items: center centering horizontally)
.box {
  height: 150px;
  width: 400px;
  background: #000;
  font-size: 18px;
  font-style: oblique;
  color: #FFF;
  display: flex;
  flex-direction: column;
  justify-content: center;
  /* vertically aligns items */
  align-items: center;
  /* horizontally aligns items */
}
p {
  margin: 5px;
  }
<div class="box">
  <p>
    When flex-direction is column...
  </p>
  <p>
    "justify-content: center" - vertically aligns
  </p>
  <p>
    "align-items: center" - horizontally aligns
  </p>
</div>
 
 
A good place to start with Flexbox to see some of its features and get syntax for maximum browser support is flexyboxes
Also, browser support nowadays is very good: caniuse
For cross-browser compatibility for display: flex and align-items, you can use the following:
display: -webkit-box;
display: -webkit-flex;
display: -moz-box;
display: -ms-flexbox;
display: flex;
-webkit-flex-align: center;
-ms-flex-align: center;
-webkit-align-items: center;
align-items: center;