In one of my previous projects i was instructed to override Wordpress function wp_mail() with custom API. I was surprised how easy it is in Wordpress. I was looking for simple solution in Wordpress, and i found it in file wp-includes/pluggable.php (where is function wp_mail() defined). Obviously Wordpress developers thinking a lot about usability for other developers, and they simply allow override the function by defining your own function before wp-includes/pluggable.php is included. So you can simply write your own plug-in overriding the function wm_mail().

You can use following code as template for your own wp_mail() override. Don't forget change plug-in name, description, author, author uri, plugin uri. Then use replace yourplugin_ prefix with your own plug-in prefix. Also check the code of both functions, and add original source code from function wp_mail() in your function wp_mail() defined in your plug-in.

/*
Plugin Name: Your plug-in
Description: Your plug-in description
Version: 1.0
Author: yourname
Author URI: http://yourweb.com
Plugin URI: http://pluginweb.com
*/

/**
 * Check if this plug-in is enabled
 * // YOU PROBABLY WOULD LIKE TO CHANGE THIS TO SOMETHING ELSE
 */
function yourplugin_enabled() {
    return 1;
}

/**
 * Send email, using phpmailer From, Subject, Body, and $to (phpmailer doesn't have public access to recipients)
 * PLEASE NOTE THIS CODE MAY NOT ACTUALLY WORK BECAUSE WASN'T TESTED
 */
function yourplugin_send( $phpmailer, $to ) {
    if ( is_array( $to ) ) {
        $to = implode( ',', $to );
    }
    $headers = 'From: ' . $phpmailer->From;
    mail($to, $phpmailer->Subject, $phpmailer->Body, $headers);
}

// YOU WILL HAVE CHECK IF wp_mail() IS NOT DEFINED BY WORDPRESS CORE OR SOMEWHERE ELSE
if ( yourplugin_enabled() && !function_exists('wp_mail') ) {

/**
 * This was wp_mail() funtion from Wordpress 3.2.1
 *
 * @param string|array $to Array or comma-separated list of email addresses to send message.
 * @param string $subject Email subject
 * @param string $message Message contents
 * @param string|array $headers Optional. Additional headers.
 * @param string|array $attachments Optional. Files to attach.
 * @return bool Whether the email contents were sent successfully.
 */
function wp_mail( $to, $subject, $message, $headers = '', $attachments = array() ) {
    // YOU PROBABLY WILL WANT LEFT WORDPRESS ORIGINAL CODE HERE
    // LOOK FOR THE END OF THIS FUNCTION AND REPLACE $phpmailer->Send() with your function

    // Send!
    try {
        //$phpmailer->Send();
        return yourplugin_send( $phpmailer, $to );
    } catch ( phpmailerException $e ) {
        return false;
    }

} // end wp_mail

} // end yourplugin_enabled()