As noted by many others, most connections between servers are encrypted, but the servers themselves can read the messages. In fact, the servers MUST read the messages in order to get the headers. The headers and the content are all sent together, so if a particular system can read the headers then it can also read the content, which includes the attachments.
Attachments are sent encoded via some method such asbase64. That makes it possible to send binary files but doesn't provide any actual security. A human looking at a raw email with an attachment will see gibberish for the attachment, but any email program sees it as an attached file.
But the biggest catch is that while mail transport mechanisms (e.g., SMTP) only look at headers, there are plenty of modern systems that require access to attachments and examine both text/html content and attachments. Some are good - e.g., filtering out spam and viruses. Some are annoying - reading messages to serve targeted advertising. And some may be downright evil - reading email messages and attachments to harvest confidential information.
Which means that unless you use separate encryption - that means either encrypting the entire email contents or encrypting attachments and keeping any critical information out of the email text, or using a secure (https) system for online messages to a specific company (that means a system hosted by/for that company - not a simple webmail system that lets you send to anyone) - you should not:
- Send critical information - e.g., passwords and other credentials, credit card or other banking details - in email text.
- Send critical information in an attachment, whether plain text or a scanned image.
- Send critical information via fax unless you send via phone (instead of via email-to-fax) and are 100% certain that the recipient receives via phone (instead of fax-to-email).
This last one is kind of funny - plenty of medical offices and some other companies insist on faxing sensitive information because "email isn't secure enough". They are correct about email, but they ignore the fact that many people who still have a fax number receive the calls via a fax-to-email service.