At Linux in the long run I expressed the opinion that Linux in general could suffer when Linus Torvalds steps aside or dies. That opinion is generally unpopular with the Linux community, but I think it's defensible.
Apple
But before getting to that, I need to explain that I do think that Linux has a lot less to fear from succession than Apple does. Right now, Apple is riding high, gaining ground regularly and stealing both Microsoft and Unix users right and left. It's not just iPods and iPhones; OS X is a power to be reckoned with. I can guarantee that none of this would have happened without the vision and strong control of Steve Jobs. And when Steve is gone, my bet is that Apple will slide back to near oblivion very quickly.
Oh, there will be momentum. Jobs has built a great product line and that could pull them along for a few years without him. But unless someone equally strong minded and equally gifted takes the reins, Apple will falter.
Microsoft
I think Microsoft is going to suffer no matter what. What they actually need is a Steve Jobs, but their board isn't likely to appoint one even if one could be found. However, "suffering" in Microsoft's case might mean slipping a bit: if Apple and Linux fall behind, and nothing else fills the void, Microsoft junk can continue to reign just because nothing else is there to fight them. Let's hope that is not the case: if Apple and Linux can keep up the pressure, Microsoft WILL slide downward.
Linux
The "succession doesn't matter" arguments boil down to demonstrating that Linus Torvalds doesn't do all that much now, so succession really won't change much. Defenders are also quick to argue that Linux is only responsible for the kernel anyway and that most of the obstacles to widespread popularity come in other areas, like the Desktop. Those arguments definitely have truth in them, but there's more to it.
First, the "it's only the kernel", because that's the weakest: without excellence in the kernel, everything else falls apart. You can't ever hope to have the slickest, most user friendly, absolutely the grinchiest desktop if you don't have a strong and reliable kernel underneath. If the Linux kernel gets screwed up by politicking, in-fighting and neglect, Linux as a whole will suffer.
But it won't, right? It's all decentralized now, it doesn't really need Linus.
Maybe. I want to believe that as much as anyone else, and perhaps even more so: I think open source is critical to our future and that we will lose a lot if proprietary systems regain their absolute dominance. But I think that the "nothing to worry about" arguments neglect two basic elements.
The first is charisma. Linus Torvalds IS the face of Linux just as Steve Jobs is the face of Apple. Outside of the kernel mailing lists, nobody knows any other name. That's important, because perception is reality: if the business world sees Linux as leaderless and rudderless, faith will be lost. Again, here it's not a matter of reality, it's perception that matters. Even if a strong leader steps up to take the reins, he or she will be an unknown, and that can shake confidence.
Secondly, I suspect it's unlikely that a strong leader will emerge. There are too many strong willed individuals capable of taking over, so there likely will be extreme bickering and fighting. That may resolve without serious damage, but it could also lead to dreaded forks or worse, management by committee. And that last is probably the thing that should be feared the most. A committee won't screw up the kernel by making bad technical decisions as a popular but incompetent leader might; no, they'll screw it up by inaction.
That's the real danger here. A moribund kernel lagging behind other developers needs will either push them to other platforms or tempt them to fork.
None of this HAS to happen. My hope is that it WON'T happen. But it CAN.