imap_fetchstructure

Here is code to parse and decode all types of messages, including attachments. I've been using something like this for a while now, so it's pretty robust.

<?php
function getmsg($mbox, $mid) {
    / input $mbox = IMAP stream, $mid = message id
    / output all the following:
    global $charset, $htmlmsg, $plainmsg, $attachments;
    $htmlmsg = $plainmsg = $charset = '';
    $attachments = array();

    / HEADER
    $h = imap_header($mbox, $mid);
    / add code here to get date, from, to, cc, subject...

    / BODY
    $s = imap_fetchstructure($mbox, $mid);
    if (!$s->parts)  / simple
        getpart($mbox, $mid, $s, 0);  / pass 0 as part-number
    else {  / multipart: cycle through each part
        foreach ($s->parts as $partno0=>$p)
            getpart($mbox, $mid, $p, $partno0+1);
    }
}

function getpart($mbox, $mid, $p, $partno) {
    / $partno = '1', '2', '2.1', '2.1.3', etc for multipart, 0 if simple
    global $htmlmsg, $plainmsg, $charset, $attachments;

    / DECODE DATA
    $data = ($partno)?
        imap_fetchbody($mbox,$mid,$partno):  / multipart
        imap_body($mbox,$mid);  / simple
    / Any part may be encoded, even plain text messages, so check everything.
    if ($p->encoding==4)
        $data = quoted_printable_decode($data);
    elseif ($p->encoding==3)
        $data = base64_decode($data);

    / PARAMETERS
    / get all parameters, like charset, filenames of attachments, etc.
    $params = array();
    if ($p->parameters)
        foreach ($p->parameters as $x)
            $params[strtolower($x->attribute)] = $x->value;
    if ($p->dparameters)
        foreach ($p->dparameters as $x)
            $params[strtolower($x->attribute)] = $x->value;

    / ATTACHMENT
    / Any part with a filename is an attachment,
    / so an attached text file (type 0) is not mistaken as the message.
    if ($params['filename'] || $params['name']) {
        / filename may be given as 'Filename' or 'Name' or both
        $filename = ($params['filename'])? $params['filename'] :
$params['name'];
        / filename may be encoded, so see imap_mime_header_decode()
        $attachments[$filename] = $data;  / this is a problem if two files have same name
    }

    / TEXT
    if ($p->type==0 && $data) {
        / Messages may be split in different parts because of inline
attachments,
        / so append parts together with blank row.
        if (strtolower($p->subtype)=='plain')
            $plainmsg .= trim($data) ."\n\n";
        else
            $htmlmsg .= $data ."<br><br>";
        $charset = $params['charset'];  / assume all parts are same charset
    }

    / EMBEDDED MESSAGE
    / Many bounce notifications embed the original message as type 2,
    / but AOL uses type 1 (multipart), which is not handled here.
    / There are no PHP functions to parse embedded messages,
    / so this just appends the raw source to the main message.
    elseif ($p->type==2 && $data) {
        $plainmsg .= $data."\n\n";
    }

    / SUBPART RECURSION
    if ($p->parts) {
        foreach ($p->parts as $partno0=>$p2)
            getpart($mbox, $mid, $p2, $partno.'.'.($partno0+1));  / 1.2, 1.2.1, etc.
    }
}
?>

Assuming $struct = imap_fetchstructure($x,$y);

It is important to note that if a message has NO attachements, $struct->parts is an empty array, and $struct->bytes has a value.  If a message as ANY attachements, $struct->bytes ALWAYS = 0. To get the size of the primary body, you have to call structure->part[0]->bytes.  To get the size of the whole message, either strlen(imap_body) or add up the ->bytes of all the parts.

Another interesting note: 
When there is body text and no attachements:
count($struct->parts) = 0
When there is body text and 1 attachement:
count($struct->parts) = 2

These imap functions could really use better documentation. Like giving the meathods for the dparameter and parameter classes...

Point of clarification:

The seventh primary body type is not "Other" as documented, but actually "Model".  This encompasses IGES, VRML, MESH, DWF, etc.