How to remove Admin/User Bar on WordPress 3.1?

Try putting this in your theme’s function.php:

remove_action('init', 'wp_admin_bar_init');

If you also want to remove the enable/disable option in user preferences, try this instead:

<?php function hide_admin_bar_settings() {
?>
<style type="text/css">
	.show-admin-bar { display: none;}
</style>
<?php
}

function disable_admin_bar() {
    add_filter( 'show_admin_bar', '__return_false' );
    add_action( 'admin_print_scripts-profile.php', 'hide_admin_bar_settings' );
}
add_action( 'init', 'disable_admin_bar' , 9 );
?>

Which version of the code above did you try?