A client of mine recently used a plug-in similar to Widget Context to accomplish this.
Rather than create different sidebars you just define what contexts you want your widgets to show up in. So if you have a set of widgets you want to show up on a specific page, you mark them to only show up on that page. But it allows you to continue using widgets that show up on every page/post if you want.
The convenience of this plug-in is that you don’t have to code anything, and it’s got a fairly intuitive UI you can put in the hands of your own clients.