Most of those horror stories won't happen if you go through the upgrade cycle once a year. A year's worth of chances is manageable for whoever is maintaining the software, three or five years worth of browser features will make the heart of any developer sink.
It is a fallacy to believe that you can stave off updating a modern internet connected browser indefinitely; the IE6/7/8 hell has driven that lesson home in the industry, and security updates are a necessity. If you do need to stay with one particular browser version, then you use a virtual machine or some other properly sandboxed environment to offer it. You can keep running IE6 on Windows XP for as long as you like with a VM that thinks its the year 2003 and which for some reason can only reach http://oldunmaintainedapp.legacy.intranet.example.com. That's fine too (although I would hate to maintain that solution).
It is a fallacy to believe that you can stave off updating a modern internet connected browser indefinitely; the IE6/7/8 hell has driven that lesson home in the industry, and security updates are a necessity. If you do need to stay with one particular browser version, then you use a virtual machine or some other properly sandboxed environment to offer it. You can keep running IE6 on Windows XP for as long as you like with a VM that thinks its the year 2003 and which for some reason can only reach http://oldunmaintainedapp.legacy.intranet.example.com. That's fine too (although I would hate to maintain that solution).