You can apply this CSS to the inner <div>:

#inner {
  width: 50%;
  margin: 0 auto;
}

Of course, you don't have to set the width to 50%. Any width less than the containing <div> will work. The margin: 0 auto is what does the actual centering.

If you are targeting Internet Explorer 8 (and later), it might be better to have this instead:

#inner {
  display: table;
  margin: 0 auto;
}

It will make the inner element center horizontally and it works without setting a specific width.

Working example here:

#inner {
  display: table;
  margin: 0 auto;
  border: 1px solid black;
}
#outer {
  border: 1px solid red;
  width:100%
}

<div id="outer">
  <div id="inner">Foo foo</div>
</div>

EDIT

With flexbox it is very easy to style the div horizontally and vertically centered.

#inner {  
  border: 1px solid black;
}
#outer {
  border: 1px solid red;
  width:100%;
  display: flex;
  justify-content: center;
}

<div id="outer">
  <div id="inner">Foo foo</div>
</div>

To align the div vertically centered, use the property align-items: center.

Warning! This answer is too old and doesn't work on modern browsers.

_{I'm not the poster of this answer, but at the time of writing this, this is the most voted answer by far in both positive and negative votes (+1035 -17), and it's still marked as accepted answer (probably because the original poster of the question is the one who wrote this answer).}

As already noted many times in the comments, this answer does not work on most browsers anymore (and seems to be failing to do that since 2013).

After over an hour of tweaking, testing, and trying different styles of markup, I think I may have a decent solution. The requirements for this particular project were:

1. Inputs must be on their own line.
2. Checkbox inputs need to align vertically with the label text similarly (if not identically) across all browsers.
3. If the label text wraps, it needs to be indented (so no wrapping down underneath the checkbox).

Before I get into any explanation, I'll just give you the code:

label {
  display: block;
  padding-left: 15px;
  text-indent: -15px;
}
input {
  width: 13px;
  height: 13px;
  padding: 0;
  margin:0;
  vertical-align: bottom;
  position: relative;
  top: -1px;
  *overflow: hidden;
}

<form>
  <div>
    <label><input type="checkbox" /> Label text</label>
  </div>
</form>

Here is the working example in JSFiddle.

This code assumes that you're using a reset like Eric Meyer's that doesn't override form input margins and padding (hence putting margin and padding resets in the input CSS). Obviously in a live environment you'll probably be nesting/overriding stuff to support other input elements, but I wanted to keep things simple.

Things to note:

• The *overflow declaration is an inline IE hack (the star-property hack). Both IE 6 and 7 will notice it, but Safari and Firefox will properly ignore it. I think it might be valid CSS, but you're still better off with conditional comments; just used it for simplicity.
• As best I can tell, the only vertical-align statement that was consistent across browsers was vertical-align: bottom. Setting this and then relatively positioning upwards behaved almost identically in Safari, Firefox and IE with only a pixel or two of discrepancy.
• The major problem in working with alignment is that IE sticks a bunch of mysterious space around input elements. It isn't padding or margin, and it's damned persistent. Setting a width and height on the checkbox and then overflow: hidden for some reason cuts off the extra space and allows IE's positioning to act very similarly to Safari and Firefox.
• Depending on your text sizing, you'll no doubt need to adjust the relative positioning, width, height, and so forth to get things looking right.

Hope this helps someone else! I haven't tried this specific technique on any projects other than the one I was working on this morning, so definitely pipe up if you find something that works more consistently.

Warning! This answer is too old and doesn't work on modern browsers.