The problem seems to be with the plugin trying to use an SSE instruction without checking if the processor actually supports it. When the instruction is not supported, the Flash plugin crashes and takes the browser with it.
The problem is present in both the ActiveX plugin and the Netscape plugin. This means that it will crash, Firefox, IE, Opera, Safari and any other browser that uses the plugin. What's worse is that 126.96.36.199 was just released and it still has the problem.
It looks like Adobe is dropping support for non-SSE processors. If so, this would make them just as bad as Microsoft and its Silverlight plugin.
The Silverlight plugin initially worked fine on my PII, but they pulled the plugged on that when releasing the first final and now Silverlight won't even install. But, even if you workaround it, the plugin truly doesn't support non-SSE processors anymore and zero Silverlight sites work properly (the embedded plugin window will be blank). Safari Win32 actually didn't support non-SSE processors at first either, but they're cool and fixed it.
As a workaround, you can use Flash 9r47, but it has security holes. So, it's a toss-up between security and stability. However, a lot of sites are now requiring 188.8.131.52 or newer to even work, so you might not have choice of stability.
Now, if you have a non-SSE processor, maybe it's time to upgrade (even an old PIII should do the trick). Or, maybe it's time to shift some tasks to one of your newer machines. However, I think that's besides the point. There are still zillions of users of non-SSE processors and just forgetting about them is not good (especially when the newest version of the plugin that works right has security flaws).
I think it's just a bug, but since users on the Flash player forums have been complaining and filing reports since 184.108.40.206 came out and it still isn't fixed, I'm beginning to think it's intensional. I expect to see the Flash installer start saying "Processor not supported" on my PII machine before too long.
Maybe "Don't break the web!" should apply to the Silverlight and Flash plugins also!