Display posts of the last 7 days

In addition to birgire’s solution, as of WordPress 3.7, you can use Date parameters.

Your arguments would look like this to filter posts from the last 7 days:

$args = array(
    'post_type' => 'post',
    'post_status' => 'publish',
    'orderby' => 'date',
    'order' => 'DESC',

    // Using the date_query to filter posts from last week
    'date_query' => array(
        array(
            'after' => '1 week ago'
        )
    )
);