Get emails of register user in WordPress

The user table column you are searching for is user_email

$emails = new WP_User_Query( array(
    'fields'  => array( 'display_name', 'user_email', ), // you don't want everything, right?
    'orderby' => 'email',                                // 'user_email' works as well
    'order'   => 'ASC',                                  // default: 'DESC'
    'number'  => 10,                                     // total amount of users to return
    'offset'  => 0,                                      // use in combination with 'number' to page results
    'search'  => '*@*',
    'search_columns' => 'user_email',
    'blog_id' => get_current_blog_id(),                  // Multisite needs that, allows cross site search
    'role'    => 'subscriber',                           // in case you want to exclude admins, etc.
    'exclude' => array( 1, ),                            // Blacklist user IDs
) );

Then there’s the filter pre_user_query that you can use to get the whole class back. You can also use it to debug your query:

<?php /* Plugin Name: Debug User Query */
add_filter( 'pre_user_query', function( &$query )
{
    var_dump( $GLOBALS['wp_query']->last_query );
    return $query;
} );