The SmtpClient send method returns void. Is there any way to get the server response? Do I just assume it was successful unless it throws an exception?
The class I'm referring to... http://msdn.microsoft.com/en-us/library/system.net.mail.smtpclient.aspx
To answer your second point, yes, all you can do is assume it's successful - meaning it got the message to the server and the server accepted it, unless you get an exception.
You probably already know the rest of this, but just in case...
From there, the email could get lost and not delivered any number of ways. Your server may accept it and decide not to send it, or accept it and lose power before crashing. It may get blocked by a spam filter along the way, etc.
You can think of an email as being similar to a regular piece of mail in that it passes through several hands between the sender and the recipient. From your code, you can only confirm that it got to the SMTP server you're using to send, which is similar to handing it to a teller at the post office. You don't know (or need to know) how the message is routed from there. it could be by air, ground, or carrier pigeon. You're out of the equation - you don't need to know how it gets sent, just that you trust that they know how to send it. (The same can be said for an email.)
If you need to confirm that the recipient opened it, there are ways of embedding an image in an HTML message on your server and tracking in your logs when that image is accessed, etc. (Google email tracking and email open tracking)
On the other hand...
If the server rejects it, then you do get a server response in a manner of speaking - there should be an error code and a description in the error, which you can use to troubleshoot why it didn't make it, or use error handling to try another route, etc.