Yes. Take a look at the link to document content type. That lets you add a
link to an HTML address of a document stored in another document library to
an existing document library.

If it is an html link, wouldn't the user need rights to the other directory?

I don't see that option anywhere. When I go to a documents folder, I see the
button for new, which allows either a new document or new folder - and the new
document action will only work with a "sharepoint compatible application", which
I don't seem to have (even though I have office 2010).

It's a content type. You need to go into advanced settings in the list and
enable management of content types. Then add the content type. Once that's done
you'll see it on the new button in the library.

is there a way (do you know?) that I can get the link icon in the "Type"
column to display the document icon instead of a link icon? I don't want it to
look like a link.

No way to change that icon that I’m aware of without custom programming.

Am I correct in assuming that you need to use a list, rather than a document
library, if you want the option of storing the document itself, or just storing
a hyperlink? If you use a document library, you can't get away with just the
hyperlink, because it is document centric. And if you store the document, then
it is stored as an attachment. Or is there something that I missed?

No. the Link to document content type works in a document library just like
a document. It doesn't require a list. It is so you can put a hyperlink to
a document stored elsewhere in a document library.

Tried it out this morning, and works great - thanks to both of you. This is
really useful! Belongs on a list of top 10 SP tips.

The link to the document seems to work just fine using document libraries. When
I click on the link, it works just like I would have clicked on a document.

There is a Content Type named "Link to Document" which does exactly what you
want to do.

In SharePoint 2007, hover the file you want to view somewhere else. Select
Send To from the drop down list and enter the URL for the site you want to send
it to. The new location will have a "copy" of the file. You can keep the
connection or break the link. No more duplication.

Thanks, but "send to" is the same as duplication. I think creating a link is
the only way to have in in two places at once with only a single file.