jQuery Ajax POST example with PHP

I am trying to send data from a form to a database. Here is the form I am using:

<form name="foo" action="form.php" method="POST" id="foo">
    <label for="bar">A bar</label>
    <input id="bar" name="bar" type="text" value="" />
    <input type="submit" value="Send" />

The typical approach would be to submit the form, but this causes the browser to redirect. Using jQuery and Ajax, is it possible to capture all of the form’s data and submit it to a PHP script (an example, form.php )?