See pkamb's answer for current implementation!
Ok, so this was largely implemented, albeit in a rather annoying fashion, via the notifications you got when a question you'd "favorited" was modified.
But then came The Global Inbox (Eeek...), and that went away. There is a proposal to bring favorite notifications back, inboxified and meaner than ever - if you yearn to watch, peeping-tom-style, questions that are not your own, I would strongly advise you to up-vote this feature request.
Note that comment notification is now flexible enough to automatically notify folks of responses to posts they've commented on in the most common scenarios (those involving a response from the owner of the post). "Subscribing" to comment threads is probably not going to happen, at least in the form described here - it would tend to encourage lengthy comment discussions, which we'd much rather bump into chat.
In light of these events, and per Pekka's request, I'm marking this status-deferred - again, if you want to follow activity on a question, let your votes pour down upon this.