News is still flooding in on this, so I'll be brief here and follow up when we know more. The question of "what will happen when we kill bin Laden?" has been the topic of my research for the last year-plus. I've attempted to answer this question in my undergraduate thesis and a series of conference papers that resulted from it. The March 31 version of the paper, presented at WPSA, is available via the Social Science Research Network.
In February I also gave a poster presentation in Austin, attempting to answer the question above.
So what do I predict will happen? Since bin Laden is a Tier One leader, I don't think we'll see any major backlash in violence in the short-term (3-6 months). However, I offer this with the huge caveat that al-Qaeda is unique in its corporate structure, networking with other groups, and (perceived) capabilities. If this had happened seven or eight years ago I think we would've seen huge protests from Jeddah to Jakarta, but now Arab youth seem to have other things on their mind.
Comments, follow-up questions, and even mildly informed disagreement are all welcome.
(Yes I know, Indonesia is not Arab.)