query recent posts from several categories

simply add this above your loop

$args = array(
    'posts_per_page' => 10,
    'category__in' => array( 2, 6 ), //change and add the category ids here
    'orderby' => 'date',
    'order' => 'ASC')
query_posts($args);

and you can read more about query_posts Parameters http://codex.wordpress.org/Function_Reference/WP_Query#Parameters

Update

By popular demand 🙂
here is another example to doing the same but using tax_query

$args = array(
    'tax_query' => array(
        array(
            'taxonomy' => 'category',
            'field' => 'slug',
            'terms' => array('category1','category2') ////change and add the category slugs here
        )
    )
    'posts_per_page' => 10,
    'orderby' => 'date',
    'order' => 'ASC')
query_posts($args);