I want to send one of my Facebook friends an e-mail, but I don't have his email-address.
It's rather personal, so I don't want to send it via Facebook if possible.
How can I get his e-mail address if it's not listed in his Profile?
This would go against the privacy settings on Facebook. If you need a private communication channel, I suggest you send them a private message with your own address, and ask them to contact you.
If the e-mail address is not listed in the Profile, there is no way you can get it From Facebook (unless you do some kind of hacking).
The only way to get his email address is to contact him (either through Facebook or some other source) and get his email address.
OR ELSE Facebook does has the option of sending Private Messages to it's users - from the User's point of view it works exactly as e-mail and from all point of views it's as secure and private as e-mails.