Exclude active events from Event Espresso event lists (only show upcoming events). You can add this to a functions or into your WordPress theme's functions.php file.

functions.php

<?php
//* Please do NOT include the opening php tag, except of course if you're starting with a blank file

add_action( 'pre_get_posts', 'my_custom_ee_posts_where_hook' );
function my_custom_ee_posts_where_hook ( $query ) {
    if (  
        isset( $query->query_vars['post_type'] ) && 
        ( $query->query_vars['post_type'] == 'espresso_events' || 
            ( is_array( $query->query_vars['post_type'] ) && 
                in_array( 'espresso_events', $query->query_vars['post_type'] ) ) ) && 
        ! $query->is_singular ) 
    {
        add_filter( 'posts_where', 'my_custom_ee_posts_where' );
    }
}
function my_custom_ee_posts_where( $SQL ) {
    $SQL .=  ' AND ' . EEM_Datetime::instance()->table() . '.DTT_EVT_start > "' . current_time( 'mysql', true ) . '" ';
    return $SQL;
}