Asynchronously sending Emails in C#?

As it's a small unit of work you should use ThreadPool.QueueUserWorkItem for the threading aspect of it. If you use the SmtpClient class to send your mail you could handle the SendCompleted event to give feedback to the user.

ThreadPool.QueueUserWorkItem(t =>
{
    SmtpClient client = new SmtpClient("MyMailServer");
    MailAddress from = new MailAddress("[email protected]", "My Name", System.Text.Encoding.UTF8);
    MailAddress to = new MailAddress("[email protected]");
    MailMessage message = new MailMessage(from, to);
    message.Body = "The message I want to send.";
    message.BodyEncoding =  System.Text.Encoding.UTF8;
    message.Subject = "The subject of the email";
    message.SubjectEncoding = System.Text.Encoding.UTF8;
    // Set the method that is called back when the send operation ends.
    client.SendCompleted += new SendCompletedEventHandler(SendCompletedCallback);
    // The userState can be any object that allows your callback 
    // method to identify this send operation.
    // For this example, I am passing the message itself
    client.SendAsync(message, message);
});

private static void SendCompletedCallback(object sender, AsyncCompletedEventArgs e)
{
        // Get the message we sent
        MailMessage msg = (MailMessage)e.UserState;

        if (e.Cancelled)
        {
            // prompt user with "send cancelled" message 
        }
        if (e.Error != null)
        {
            // prompt user with error message 
        }
        else
        {
            // prompt user with message sent!
            // as we have the message object we can also display who the message
            // was sent to etc 
        }

        // finally dispose of the message
        if (msg != null)
            msg.Dispose();
}

By creating a fresh SMTP client each time this will allow you to send out emails simultaneously.

As of .NET 4.5 SmtpClient implements async awaitable method SendMailAsync. As a result, to send email asynchronously is as following:

public async Task SendEmail(string toEmailAddress, string emailSubject, string emailMessage)
{
    var message = new MailMessage();
    message.To.Add(toEmailAddress);

    message.Subject = emailSubject;
    message.Body = emailMessage;

    using (var smtpClient = new SmtpClient())
    {
        await smtpClient.SendMailAsync(message);
    }
}