Here is a new piece by Hardt & Negri, where they reject the pronouncements of “traditional political thinkers” who say the uprisings of 2011 need leaders, parties, and ideologies.*
Until there is a party and an ideology to direct the street conflicts, the reasoning goes, and thus until the churches are filled, there will be no revolution. But it’s exactly the opposite! We need to empty the churches of the Left even more, and bar their doors, and burn them down! These movements are powerful not despite their lack of leaders but because of it. They are organized horizontally as multitudes, and their insistence on democracy at all levels is more than a virtue: it is a key to their power.
I think we need to get to the point where this kind of thinking is taken for granted, rather than something we still have to make a case for. Then we can get on with the work of experimenting with horizontal organization, learning what it means to be a multitude, and discovering the power of democracy.
*e.g. Zizek, and Jodi Dean, who is much more nuanced and thoughtful.
Path to the Possible 
Well, I hope that the thought you are expressing in your last paragraph is never the case.
Revolutions are never spontaneous, neither are they done on their own. Such an enormous task requires a lot of intelligence, effort and knowledge and a revolutionary party is what ensures that the legacy of struggle builds up from generation to generation until the society is changed. Perhaps then “horizontality” is something desirable.
Certainly revolutions are often spontaneous, unless we insist that ‘revolution’ means a workers’ party seizing the state, in which case revolution is among the last things we should seek. Of course people have to carry out revolutions, with their bodies, their intelligence, their desires, and their efforts. And of course we want struggle to accrete, we want to build a critical mass of connected entities struggling for radical change. I guess what I mean is that I hope we get to the point where we no longer think the only way to do all of this is by means of a revolutionary party. Or better still, where it has become common sense that a revolutionary party, at least as it is typically understood, is precisely the opposite of the kind of collective we hope for.
Radical advances often occur inspite of the Left, rather than as a direct result.
Personally, what I’m looking forward to is not the hegemony of horizontality but organization via non-coordination (or at least indirect coordination). In anarchist circles, for instance, there already seems to be a hegemony of a dumb version of horizontality. The result is rarely spontaneity but it’s de-intensifying opposite — endless meetings weighed down by process, and hesitancy to take action without consider the infinity of possible contingencies. Alternatively, the forms of cooperation and coordination that Hardt and Negri have so well identified as being the conditions for postmodern production are driving the rest of society. Want breaking news on the Aurora shooting? Some person live-blogging it on Reddit was the most reliable source… Yet social movements are way behind the ball — even when they’re horizontal, they still want to be constituted rather than constituent. Post-Deleuzian Tardeans have been talking about this for a while (e.g. that new UMN press book on virality), but social movement types are way behind the ball. At the most, you have ELFers talking about clandestine “copycats”. And at worst, we have people repeating Lenin when concrete moment has changed from total mobilization to cybernetics (and not even second-order cybernetics, to boot).
What does noncoordinated action have in store? Maybe the Arab Spring, or OWS. But really, it could be so much more. What that is? I either haven’t read the right stuff, or it’s so ‘now’ that my vision is fuzzy. I have a few ideas, but I’d rather hear what others have to say first.
I agree about the hegemony of horizontality–I do think such hegemony would create a soft assumptive horizontality rather than a robust one that continually has to make a case for itself. And it is not bad practice to have to reiterate the dangers of a socialist party-state politics. My comment was more out of frustration that every moment spent fighting off the Old Socialist is a moment not spent experimenting with the answers to the important questions in your last paragraph…things like (maybe) the asambleas emerging in some Madrid neighborhoods, or…