Problems sending mails to Hotmail,Gmail... using SMTP

Hi,
I'm doing a web application that allows email through an SMTP service. I have some SMTP servers (including my university and work) that allow receiving mail via SMTP. But I want to go further and bring this application to send emails to hotmail, gmail etc ... which it is impossible for me as an exception "5.1.7 Unable to relay". It took time looking but I can not find any solutions consistently. I would appreciate help.
Here is the code below (it fails):
MailMessage msg = new MailMessage();

            msg.To.Add(new MailAddress("fedex85@hotmail.es"));

            msg.From = new Mail ...