Discussed in this thread and this one, and this Wikipedia article.
Of course you don’t have a collective brain in these kinds of situations. But I’m sympathetic to the view that in these situations you can have collective intentions which don’t simply boil down to the collection of all the individual intentions.
Actually, the claim to fame of one of the profs sitting on my committee is that she has developed a theory of collective intentionality. You can have groups which have beliefs, intentions, desires, (I would argue memories), and so on, even when none of the individuals in the group shares these beliefs, intentions, desires and so on. The usual situation is that some of the members do share these beliefs etc., but the point is, that’s not what constitutes the group belief. Rather, the group belief is constituted by a bunch of explicit and implicit agreements between the individuals to (for example) avow the belief when speaking for the group, and so on.
That’s one way you can have something like a “collective mind” (though she is always very careful to distinguish what she is talking about from the idea of any kind of “oversoul,” though I am not sure I think she is right to be concerned to make this distinction.)
Married couples probably have collective intentions in much the same way, but I think there’s another way in which married couples (and many other kinds of groups) can have something like a “group mind” or “collective intention.” A mind is something that cognizes. What cognition is is controversial, but I would argue that it’s goal-directed information processing undertaken as a function of a self-maintaining dynamic system. (Each term in what I just said requires careful definition of course but let’s skip it for now. Esp. since I haven’t necessarily thought through each term in complete detail!) Obviously, then, human beings cognize. But arguably, several kinds of social groups form cognitive systems of their own on a definition like this. They can be self maintaining dynamic systems, and there can be information processing going on as a function of this self maintenance. Indeed, the information processing need not happen only inside particular individuals’ craniums. It could happen in the interactions between them. Arguably, then, such groups form cognizing agents of their own, and this would be another kind of group mind. (My prof’s collective intentionalities may be a sub-type of this.)
As it stands, these kinds of collective cognitive agents are generally very simple, as cognitive agents go. (But they let us individual humans accomplish a lot that we as individual humans couldn’t accomplish by ourselves.) But as the technology for inter-cranial cognition becomes more and more complex and interesting, the complexity of these collective cognitive agents is likely to increase, and they may take on more and more of the characteristics that make us think of them as coherent minds, even conscious minds. That’s just speculation on my part, of course. But it’s a speculation a few cognitive scientists and a lot of science fiction authors share 
, so in that sort of gee-whiz way has the feel of the kind of speculation that’s very likely to lead to something real in the future.
Would this be a good or a bad thing? Well it has to be done the right way. I have another prof who started taking this kind of thing seriously in the late 80’s and early 90’s as he started looking at how this new thing called “the internet” was changing the way people interact with each other. He’s got a very interesting but very paranoid piece in which he argues that we should watch for the development of this kind of “overmind” constituted by connections people make with each other through the internet and the actions they are enabled to take by this connection, and he argues that we should be careful to destroy such an overmind before it has a chance to develop any kind of power. He thinks the existence of such an overmind is almost completely (but not logically) incompatible with freedom and even (for some reason I haven’t understood) consciousness for the sub-cognizers within such an overmind. His view is, basically, that the perfect human Utopia does have a kind of overmind (or anyway, cognizing agent constituted by the activity of humans communicating with each other) but that it is far too easy to slip up and develop such an overmind in the wrong way and lose individual personhood as a result. So he says down with the internet if it ever comes to that. Interesting guy! 
What’s the right way then? I haven’t really given it a lot of thought, but I think it’s clear that to the extent that the communication networks we participate in somehow interfere with our own agency or even our own coherent identity as persons, something is going wrong. Does that happen? Perhaps so, in some ways. Openness to lots of communication, on the one hand, gives one more of the ability to get a handle on things, but on the other hand, makes one more vulnerable to outside control to the extent that anyone (individual or collective) can take control of the information you have access to. Also, openness to communication can easily lead to an en-fuzz-ening of one’s personal boundaries–the more communication channels, the more ubiquitous this en-fuzz-ening can be. And the more one involves one’s personal transaction with channels of communication (i.e. online commerce etc) the more one makes oneself vulnerable to outside interference and even control. But I don’t think one should be paranoid about this kind of thing, rather, one should approach it as a challenge which can be overcome through technologies.
I’m rambling.
Anyway, yes, I think there can be “collective minds,” both through social interaction and through technological innovations in communication (often both come together in the making of collective cognitive agents) and I think this can be a good thing but that one should be careful about it, as there is a real danger of the destruction of what we care about when we care about personal identity and personal coherence.
-FrL-
The boards went down for a while while I was trying to edit my post. I wanted to edited by adding “presentational” as bolded above and by adding the footnote as above.
-FrL-
Personally, we happen to like it! 
I’m another person who thinks it would depend entirely on what variety of collective mind you ended up with. When and if such a thing becomes doable, I expect that there will be many such minds, of different varieties.
This was played with in the Star Trek: Voyager episode “Collective.”
The Borg Queen apparently is not so much the Collective’s leader as its personification-and-voice.
To be fair, there are between 3-5 quite different interpretations of the Borg. They were originally conveived as a machine-assisted group cyborgs with no interest in other species, who created children and plgged them into the machine interface. Then they were willing to forcibly assimilate a human to gain his knowledge. Then they were master assimilators and did this all the time, and even had special technology to do it, and they had a Queen and Time Travel and all. Then they were actually the galaxy’s wusses and were smacked around by everybody with a gun and a bad attitude and…
Y’know, I don’t even want to go into this.
sigh A world without a collective effort to give me an orgasm is torture enough.
[kneels and dabs hankie [with stains better not inquired into] at NurseCarmen’s soft sweet tears] Despair not! Henceforth, my lady, all True Dopers will make your orgasms our life’s mission unto death, by any means possible or imaginable! Who’s with me?!
While I personally find the idea of a group mind a little worrying, to say the least. My favourite fictional incarnation of this idea is the Conjoiners from the Revelation Space Series by Alastair Reynolds.
Probably much more realistically portrayed than the Borg and more likely as an outcome for humanity.
Although I’m not keen on the idea of this, given the way technology is headed it is likely that some sub-set of humanity will adopt an approach similar to this at some point in the future, assuming we survive long enough to develop the tech.
Isn’t **NurseCarmen **like, you know, a dude?
If the world wide mind, as it has been called, comes to pass, are those connected the masters, or the slaves?
They are the masters, or they are the slaves, or they are neither, depending on the style of group mind.
Could you unplug?!
Like “unplugging” from the www after a few weekend hours? Is that what inspired this possibility?
Sure, I suppose anything is possible. It all depends on what kind of group mind it is.
There was an episode of “Voyager” in which the crew found a more benign Borg-like collective, composed of former captive drones. But the episode left some doubt as to whether they would stay so begnign, with the speculation that the original Borg collective may well have started out as equally begnign. (And maybe as small, or even smaller?)
So, getting back to your thought, it’s possible that you will want to be disconnected most of the time, and will always be disconnected any time you want to be, and promptly.
Or that you will be forced to remain in, once you have joined in.
Or that you will be free to go, but permanently decide against it.
Or you will “decide” such, but it will only seem to be your decision.
**Brrrrrr! **
- TBJ