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It is (currently) essentially impossible to change the software MO uses; once MO switches to SE2.0 this might be different.
I think when MO gets SE2.0 someone can use SE API to implement something like this more nicely.
You can also post on the main meta if you want to request the feature to mark some users as favorites to get say email newsletters about their posts.
I'm still confused. What's wrong with the "recent" tab on the user page? It seems to be precisely what you're asking for.
@Scott Morrison: As far as I understand (mainly based on the other thread) the "problem" is that one would have to navigate to said page in some way; which one can find less convenient in the way one would/could do it now than it would be if one could "follow" some user(s) and, say, this would create a direct link to their "recent" tab on ones own userpage (somehow like it is for favorited questions). (Or even, but this was I think not really suggested, get a notification when one of the users one follows wrote something new, or there would be a page with all the recent contributions of all users one "follows" together and things like this.)
To be clear, I certainly do not request this and I would not even appreciate this feature existed (for reasons alluded to by Asaf Karagila), so this is only to convey my interpretation of what was meant and I can abstractly see why somebody might like to have this (even if personally I find it rather going against the idea of the site, as I see it).
Okay, that makes some sense. Perhaps I was falsely assuming that everyone sees RSS as a good solution to this sort of problem. (In fact, I used to have a Facebook account, but I haven't looked at it since the day they turned off RSS feeds, so I sympathize with not wanting to visit particular pages. That said, user pages on mathoverflow have RSS feeds!)
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