Some times it's a good idea trying to get some background about what you're willing to do. For downloading e-mails from the server you use what is called e-mail protocol. Two of the most commonly used ones are POP3 and IMAP. With this in mind you can go and search for something like
"pop3 client c#"[
^]
The
OpenPop.NET[
^] library implements the protocol and also the MIME parser.
You will find something about IMAP (client) here:
Simple IMAP CLIENT[
^] and here:
IMAP and POP3 Clients in C#[
^].
Looking at those projects you'll get part of the background you need for it.