Tavsiye için teşekkür ederim bundan sonra öyle yaparım. Söylediğiniz kodu eklediğimde sayfa üzerinde gözüken kodları aşağıda sizinle paylaşıyorum..

SMTP -> get_lines(): $data was "" 
SMTP -> get_lines(): $str is "220-web.xxx.com.tr ESMTP Exim 4.86_1 #1 Sun, 10 Apr 2016 13:40:23 +0300 " 
SMTP -> get_lines(): $data is "220-web.xxx.com.tr ESMTP Exim 4.86_1 #1 Sun, 10 Apr 2016 13:40:23 +0300 " 
SMTP -> get_lines(): $data was "220-web.xxx.com.tr ESMTP Exim 4.86_1 #1 Sun, 10 Apr 2016 13:40:23 +0300 " 
SMTP -> get_lines(): $str is "220-We do not authorize the use of this system to transport unsolicited, " 
SMTP -> get_lines(): $data is "220-web.xxx.com.tr ESMTP Exim 4.86_1 #1 Sun, 10 Apr 2016 13:40:23 +0300 220-We do not authorize the use of this system to transport unsolicited, " 
SMTP -> get_lines(): $data was "220-web.xxx.com.tr ESMTP Exim 4.86_1 #1 Sun, 10 Apr 2016 13:40:23 +0300 220-We do not authorize the use of this system to transport unsolicited, " 
SMTP -> get_lines(): $str is "220 and/or bulk e-mail. " 
SMTP -> get_lines(): $data is "220-web.xxx.com.tr ESMTP Exim 4.86_1 #1 Sun, 10 Apr 2016 13:40:23 +0300 220-We do not authorize the use of this system to transport unsolicited, 220 and/or bulk e-mail. " 
SMTP -> FROM SERVER:220-web.xxx.com.tr ESMTP Exim 4.86_1 #1 Sun, 10 Apr 2016 13:40:23 +0300 220-We do not authorize the use of this system to transport unsolicited, 220 and/or bulk e-mail. 
SMTP -> get_lines(): $data was "" 
SMTP -> get_lines(): $str is "250-web.xxx.com.tr Hello web.xxx.com.tr [105.302.24.3] " 
SMTP -> get_lines(): $data is "250-web.xxx.com.tr Hello web.xxx.com.tr [105.302.24.3] " 
SMTP -> get_lines(): $data was "250-web.xxx.com.tr Hello web.xxx.com.tr [105.302.24.3] " 
SMTP -> get_lines(): $str is "250-SIZE 52428800 " 
SMTP -> get_lines(): $data is "250-web.xxx.com.tr Hello web.xxx.com.tr [105.302.24.3] 250-SIZE 52428800 " 
SMTP -> get_lines(): $data was "250-web.xxx.com.tr Hello web.xxx.com.tr [105.302.24.3] 250-SIZE 52428800 " 
SMTP -> get_lines(): $str is "250-8BITMIME " 
SMTP -> get_lines(): $data is "250-web.xxx.com.tr Hello web.xxx.com.tr [105.302.24.3] 250-SIZE 52428800 250-8BITMIME " 
SMTP -> get_lines(): $data was "250-web.xxx.com.tr Hello web.xxx.com.tr [105.302.24.3] 250-SIZE 52428800 250-8BITMIME " 
SMTP -> get_lines(): $str is "250-PIPELINING " 
SMTP -> get_lines(): $data is "250-web.xxx.com.tr Hello web.xxx.com.tr [105.302.24.3] 250-SIZE 52428800 250-8BITMIME 250-PIPELINING " 
SMTP -> get_lines(): $data was "250-web.xxx.com.tr Hello web.xxx.com.tr [105.302.24.3] 250-SIZE 52428800 250-8BITMIME 250-PIPELINING " 
SMTP -> get_lines(): $str is "250-AUTH PLAIN LOGIN " 
SMTP -> get_lines(): $data is "250-web.xxx.com.tr Hello web.xxx.com.tr [105.302.24.3] 250-SIZE 52428800 250-8BITMIME 250-PIPELINING 250-AUTH PLAIN LOGIN " 
SMTP -> get_lines(): $data was "250-web.xxx.com.tr Hello web.xxx.com.tr [105.302.24.3] 250-SIZE 52428800 250-8BITMIME 250-PIPELINING 250-AUTH PLAIN LOGIN " 
SMTP -> get_lines(): $str is "250-STARTTLS " 
SMTP -> get_lines(): $data is "250-web.xxx.com.tr Hello web.xxx.com.tr [105.302.24.3] 250-SIZE 52428800 250-8BITMIME 250-PIPELINING 250-AUTH PLAIN LOGIN 250-STARTTLS " 
SMTP -> get_lines(): $data was "250-web.xxx.com.tr Hello web.xxx.com.tr [105.302.24.3] 250-SIZE 52428800 250-8BITMIME 250-PIPELINING 250-AUTH PLAIN LOGIN 250-STARTTLS " 
SMTP -> get_lines(): $str is "250 HELP " 
SMTP -> get_lines(): $data is "250-web.xxx.com.tr Hello web.xxx.com.tr [105.302.24.3] 250-SIZE 52428800 250-8BITMIME 250-PIPELINING 250-AUTH PLAIN LOGIN 250-STARTTLS 250 HELP " 
SMTP -> FROM SERVER: 250-web.xxx.com.tr Hello web.xxx.com.tr [105.302.24.3] 250-SIZE 52428800 250-8BITMIME 250-PIPELINING 250-AUTH PLAIN LOGIN 250-STARTTLS 250 HELP 
SMTP -> get_lines(): $data was "" 
SMTP -> get_lines(): $str is "334 VXNlcm5hbWU6 " 
SMTP -> get_lines(): $data is "334 VXNlcm5hbWU6 " 
SMTP -> get_lines(): $data was "" 
SMTP -> get_lines(): $str is "334 UGFzc3dvcmQ6 " 
SMTP -> get_lines(): $data is "334 UGFzc3dvcmQ6 " 
SMTP -> get_lines(): $data was "" 
SMTP -> get_lines(): $str is "235 Authentication succeeded " 
SMTP -> get_lines(): $data is "235 Authentication succeeded " 
SMTP -> get_lines(): $data was "" 
SMTP -> get_lines(): $str is "250 OK " 
SMTP -> get_lines(): $data is "250 OK " 
SMTP -> FROM SERVER:250 OK 
SMTP -> get_lines(): $data was "" 
SMTP -> get_lines(): $str is "250 Accepted " 
SMTP -> get_lines(): $data is "250 Accepted " 
SMTP -> FROM SERVER:250 Accepted 
SMTP -> get_lines(): $data was "" 
SMTP -> get_lines(): $str is "354 Enter message, ending with "." on a line by itself " 
SMTP -> get_lines(): $data is "354 Enter message, ending with "." on a line by itself " 
SMTP -> FROM SERVER:354 Enter message, ending with "." on a line by itself 
SMTP -> get_lines(): $data was "" 
SMTP -> get_lines(): $str is "250 OK id=1bpCn1-0039De-5A " 
SMTP -> get_lines(): $data is "250 OK id=1bpCn1-0039De-5A " 
SMTP -> FROM SERVER:250 OK id=1bpCn1-0039De-5A


--R10.NET; Flood Engellendi -->-> Yeni yazılan mesaj 15:39:39 -->-> Daha önceki mesaj 13:46:23 --

Sorun nerede arkadaşlar bilenler lütfen yardımcı olabilirse sevinirim. Mail gönderimini sağlıyorum fakat mail her geldiğinde 1 tane değilde 2 tane birden geliyor. Diğer bir sorun ise mail içeriğini bir türlü post edemiyorum. Ne yaptıysam olmadı. Yardım lütfen..

    <div class="row">
    	<div class="span9">
     
        	<form id="contact-form" class="contact-form" action="<?$PHP_SELF?>" method="POST">
            	<p class="contact-name">
            		<input id="contact_name" type="text" placeholder="Ad Soyad" value="" name="name" />
                </p>
                <p class="contact-email">
                	<input id="contact_email" type="text" placeholder="Mail" value="" name="email" />
                </p>
                <p class="contact-message">
                	<textarea id="contact_message" placeholder="Mesajınız.." name="message" rows="15" cols="40"></textarea>
                </p>
                <p class="contact-submit">
                	<a id="contact-submit" onClick="Send()" class="submit" href="#">Gönder</a>
                </p>

<?php
if(isset($_POST)){
             $email=$_POST['email']; 
             $name=$_POST['name']; 
             $message=$_POST['message'];
}			 
include 'class.phpmailer.php'; //PHPMailer sinifimizi import ettik
$mail = new PHPMailer(); 

$from = "xxx@xxx.net";  //Bu dort satirda formdan gelen verileri degiskenlere aktardik   
$to = "xxx@xxx.net";
$subject = "xxx - Site";
$mail_text = '<div style="background: #eee; padding: 10px; font-size: 14px">Bu mail $name\n isimli ziyaretçi tarafından $email\n mail adresi ile siteniz üzerinden $message\n başlığı altında bırakılmıştır.</div>';

$mail->IsSMTP(); //Maili gonderecegimiz yolu belirledik
$mail->SMTPDebug = 2; //Debug islemi. 1 degeri hata ve mesaj icinken 2 degeri ile sadece mesaj olusturuluyor 
$mail->SMTPAuth = true; //SMTP kimlik dogrulamayi etkinlestirdik
$mail->Host = 'web.xxx.com';
$mail->Port = 587;
$mail->SMTPSecure = 'tls';
$mail->CharSet = 'UTF-8'; //Dil ayarlari icin UTF-8 i kullaniyoruz.
$mail->Username = $from; //mailin gonderilecegi adres
$mail->Password = 'xxx'; //mailin gonderildigi adresin sifresi
$mail->SetFrom($mail->Username, $from);
$mail->Subject = $subject; //konu
$mail->AddAddress($to); //mailin gidecegi adres
$mail -> MsgHTML($mail_text); //mailin icerigi


//Asagidaki kod blogunda mailin gonderilip gonderilmedigini kontrol ediyoruz. 

if(!$mail->Send())

{
    echo "Mailer Error: ".$mail->ErrorInfo;
}
else
{
    echo "Sent";
}

?>