If contributor has published 2 or more posts then show otherwise hide

Simpler than using the $wpdb class would be to use count_user_posts(). For instance:

$min_posts = 2;
if( count_user_posts( $post->post_author ) >= $min_posts ) {
    // display the user's posts
}

This assumes you’re in The Loop, or at the very least that $post is a WordPress Post object.

[above edited 2013-03-19 11:30 AM CDT]

Note that if you’re trying to count custom post types (and possibly pages, though I’m not sure), you’ll need to use some $wpdb magic, but there’s a code sample available at the Codex page for count_user_posts() (linked above).