There is no such thing as "downloading attachments". If some of the mail content is some Web links, then you may have something to download, but it would not be a part of a message.
Actually, the term "attachment" is highly misleading. Nothing is actually "attached" to the mail. Actually, all the mail content is just one solid block of plain text (possibly in one of Unicode UTFs or some other "encoding"), nothing else. Everything is embedded in that single block. What looks like "attachment" is actually a mail
part, separated by text separators defined in the top-level header of content type. Those "parts" have their separate groups of headers, and content types (and also "dispositions") can be different for each part. If content of the part is "binary", it is still plain text, with content encoded as base64:
http://en.wikipedia.org/wiki/Base64[
^].
You need to parse it all top to button. The format of all this is defined by the whole set of standards, so you would need to do a good amount of reading:
http://en.wikipedia.org/wiki/E-mail#Message_format[
^].
Instead, you can use some available parser. In particular, please read this tutorial:
http://www.emailarchitect.net/eagetmail/kb/csharp.aspx?cat=18[
^].
Look at this open-source parser:
http://mimeparser.codeplex.com/[
^].
—SA