How can I rotate an HTML <div> 90 degrees?

You need CSS to achieve this, e.g.:

#container_2 {
    -webkit-transform: rotate(90deg);
    -moz-transform: rotate(90deg);
    -o-transform: rotate(90deg);
    -ms-transform: rotate(90deg);
    transform: rotate(90deg);
}

Demo:

#container_2 {
  width: 100px;
  height: 100px;
  border: 1px solid red;
  -webkit-transform: rotate(45deg);
  -moz-transform: rotate(45deg);
  -o-transform: rotate(45deg);
  -ms-transform: rotate(45deg);
  transform: rotate(45deg);
}

<div id="container_2"></div>

(There's 45 degrees rotation in the demo, so you can see the effect)

Note: The -o- and -moz- prefixes are no longer relevant and probably not required. IE9 requires -ms- and Safari and the Android browser require -webkit-

Update 2018: Vendor prefixes are not needed anymore. Only transform is sufficient. (thanks @rinogo)

Use following in your CSS

div {
    -webkit-transform: rotate(90deg); /* Safari and Chrome */
    -moz-transform: rotate(90deg);   /* Firefox */
    -ms-transform: rotate(90deg);   /* IE 9 */
    -o-transform: rotate(90deg);   /* Opera */
    transform: rotate(90deg);
} 

Use transform: rotate(90deg):

#container_2 {
    border: 1px solid;
    padding: .5em;
    width: 5em;
    height: 5em;
    transition: .3s all;  /* rotate gradually instead of instantly */
}

#container_2:hover {
    -webkit-transform: rotate(90deg);  /* to support Safari and Android browser */
    -ms-transform: rotate(90deg);      /* to support IE 9 */
    transform: rotate(90deg);
}

<div id="container_2">This box should be rotated 90&deg; on hover.</div>

Click "Run code snippet", then hover over the box to see the effect of the transform.

Realistically, no other prefixed entries are needed. See Can I use CSS3 Transforms?