How do I use a {recently-updated} macro to always show results for the currently-logged-in user?

What Joseph said. Wrap the recently-updated macro in a user macro for the same ends.

In Confluence 4.x and above, something like:

<ac:macro ac:name="recently-updated">
	<ac:parameter ac:name="author">$action.remoteUser.name</ac:parameter>
</ac:macro>

In Confluence 3.x, something like:

{recently-updated:author=$action.remoteUser.name}