In Private Messages, when a sender attaches files to their messages, the e-mail mentions that the sender did so, saying:
"The following are direct links to all of the attachments that were included in this Personal Message (Please note, you must be logged in to the site in order to be able to download them): [URL to file]"
However, the links to attachments in any e-mail notification of forum posts do not appear. If this appears in PMs, I don't see why the same cannot be true for forum posts; I find it very convenient if I know immediately from an e-mail notification that a forum post has an attachment. Something like:
"The following are direct links to all of the attachments that were included in this forum post..."
I wasn't even aware they appeared in PMs. Remind me at some point in the next few days to take a look at this, I'm sure it can't be that hard if PMs can do it.
Forgot to remind you if you've gotten around to doing this yet.
I finally had a look, and there doesn't appear to be any easy way to do this, unfortunately. The code responsible for generating the email doesn't even load data on attachments (and cannot easily be modified to do so, as far as I can tell) - not even a simple yes or no to "are there any?" - so it would need extensive changes to do so.