The iPhone has native document-reading capability for several formats (DOC, TXT, RTF, etc.). You can view these attachments from the Mail application on the iPhone. These attachments are stored along with the mail message itself in the Mail application.
If you have a compatible document editing/viewing program, like Goodreader, I believe you have the option of opening compatible attachments in that program. This works on the iPad -- not sure about the iPhone, but I suspect it does.