Set div to remaining height using CSS with unknown height divs above and below

Is it possible to make the wrapper fill the window height (no scrolling) and the center div scrollable without messing around with pixels and javascript?

<div id="wrapper">
  <h1>Header</h1>
  <div id="center">
    <div style="height:1000px">high content</div>
  </div>
  <div id="footer">Footer</div>
</div>

Basically I want the header to be visible at the top and the footer to be always visible at the bottom and have a scrollable content in the center which occupies the remaning height.
The header, footer and center divs' heights are all unknown (no set px or %, i.e. variable font-size or padding). Is it possible with pure CSS?

2014 UPDATE: The modern way to solve this layout problem is to use the flexbox CSS model. It's supported by all major browsers and IE11+.

---

2012: The correct way to do this with CSS alone is to use display: table and display: table-row. These are supported by all major browsers, starting with IE8. This is not using tables for display. You'll use divs:

html, body {
    height: 100%;
    margin: 0;
}
.wrapper {
    display: table;
    height: 100%;
    width: 100%;
    background: yellow;  /* just to make sure nothing bleeds */
}
.header {
    display: table-row;
    background: gray;
}
.content {
    display: table-row;  /* height is dynamic, and will expand... */
    height: 100%;        /* ...as content is added (won't scroll) */
    background: turquoise;
}
.footer {
    display: table-row;
    background: lightgray;
}

<div class="wrapper">
    <div class="header">
        <h1>Header</h1>
        <p>Header of variable height</p>
    </div>
    <div class="content">
        <h2>Content that expands in height dynamically to adjust for new content</h2>
        Content height will initially be the remaining
        height in its container (<code>.wrapper</code>).
        <!-- p style="font-size: 4000%">Tall content</p -->
    </div>
    <div class="footer">
        <h3>Sticky footer</h3>
        <p>Footer of variable height</p>
    </div>
</div>

That's it. The divs are wrapped as you'd expect.

A cross-browser solution derived from Dan Dascalescu answer:

http://jsfiddle.net/Uc9E2

html, body {
    margin: 0;
    padding: 0;
    height: 100%;
}
.l-fit-height {
    display: table;
    height: 100%;
}
.l-fit-height-row {
    display: table-row;
    height: 1px;
}
.l-fit-height-row-content {
    /* Firefox requires this */
    display: table-cell;
}
.l-fit-height-row-expanded {
    height: 100%;
    display: table-row;
}
.l-fit-height-row-expanded > .l-fit-height-row-content {
    height: 100%;
    width: 100%;
}
@-moz-document url-prefix() {
    .l-scroll {
        /* Firefox requires this to do the absolute positioning correctly */
        display: inline-block;
    }
}
.l-scroll {
    overflow-y: auto;
    position: relative;
    height: 1000px;
}
.l-scroll-content {
    position: absolute;
    top: 0;
    bottom: 0;
    height: 1000px;
    min-height:100px;
}

<div class="l-fit-height">
    <section class="l-fit-height-row">
        <div class="l-fit-height-row-content">
            <p>Header</p>
        </div>
    </section>
    <section class="l-fit-height-row-expanded">
        <div class="l-fit-height-row-content l-scroll">
            <div class="l-scroll-content">
                <p>Foo</p>
            </div>
        </div>
    </section>
    <section class="l-fit-height-row">
        <div class="l-fit-height-row-content">
            <p>Footer</p>
        </div>
    </section>
</div>

Using overflow:auto will let you do this.

demo

So what you are talking about is a sticky footer. I went and did some more research and here is what I have for you.

<div id="wrapper" style="height:100%">
<div id="header" style="float:none;"><h1>Header</h1></div>

<div style="overflow:scroll;float:none;height:auto;">high content</div>

<div id="footer" style="clear:both;position:fixed;bottom:0px;"><h1>Footer</h1></div>
</div>

This will give you a sticky footer. The key is position:fixed and bottom:0px; Unfortunately this means it also hovers above any content in the scrollview. So far there seems to be only Javascript to figure this out but I will keep looking.