Probably your authentication (credentials) or servername/port is not correct.
Try this:
MailMessage mailMsg = new MailMessage();
mailMsg.To.Add("[email protected]");
// From
MailAddress mailAddress = new MailAddress("[email protected]");
mailMsg.From = mailAddress;
// Subject and Body
mailMsg.Subject = "subject";
mailMsg.Body = "body";
// Init SmtpClient and send on port 587 in my case. (Usual=port25)
SmtpClient smtpClient = new SmtpClient("mailserver", 587);
System.Net.NetworkCredential credentials =
new System.Net.NetworkCredential("username", "password");
smtpClient.Credentials = credentials;
smtpClient.Send(mailMsg);