CSS Image size, how to fill, but not stretch?

You can use the css property object-fit. ("sets how the content of a replaced element, such as an <img> or <video>, should be resized to fit its container.")

.cover {
  object-fit: cover;
  width: 50px;
  height: 100px;
}

<img src="http://i.stack.imgur.com/2OrtT.jpg" class="cover" width="242" height="363" />

See example here

There's a polyfill for IE: https://github.com/anselmh/object-fit

Related: object-position (specifies the alignment of an element's contents within its box.)

Enhancement on the accepted answer by @afonsoduarte.
in case you are using bootstrap

1. Providing width:100% on the style.
   This is helpful if you are using bootstrap and want the image to stretch all the available width.
   

2. Specifying the height property is optional, You can remove/keep it as you need

   .cover {
      object-fit: cover;
      width: 100%;
      /*height: 300px;  optional, you can remove it, but in my case it was good */
   }
   

3. By the way, there is NO need to provide the height and width attributes on the image element because they will be overridden by the style.
   so it is enough to write something like this.

   <img class="cover" src="url to img ..."  />
   

If you want to use the image as a CSS background, there is an elegant solution. Simply use cover or contain in the background-size CSS3 property.

.container {
  width: 150px;
  height: 100px;
  background-image: url("http://i.stack.imgur.com/2OrtT.jpg");
  background-size: cover;
  background-repeat: no-repeat;
  background-position: 50% 50%;
}

<div class="container"></div>​

While cover will give you a scaled up image, contain will give you a scaled down image. Both will preserve the pixel aspect ratio.

http://jsfiddle.net/uTHqs/ (using cover)

http://jsfiddle.net/HZ2FT/ (using contain)

This approach has the advantage of being friendly to Retina displays as per Thomas Fuchs' quick guide.

It's worth mentioning that browser support for both attributes excludes IE6-8.