Also don't forget BSD, ex: OpenBSD and NetBSD, may need to use older versions but potentially there could be compiled later versions of software than an old *nix.
I recall reading this article some time ago.
If you are thinking of an old kernel for running on a 386, I checked my current glibc 2.33, and the minimum kernel requirement is 3.2, which still supported the 386. gcc still supports the 386 today (hopefully they don't break it accidentally again). So based around that, if you carefully select what you really want to run, you could probably have a fairly recent linux software environment (who cares about the old kernel, 386 systems haven't changed much) running some useful stuff. (not everything)
But of course, the 386 was never really all that useful for linux due to lack of memory. If you can drop firefox though, you pretty much can run some kind of linux on anything. I'd be happy to lessen my use of firefox and chrome. If you look at the thread where Linus says drop the 486 support, someone responded reminding that they had not so far because 486 class systems were still being sold recently?? It seems linux still is useful on a 486. Somewhere.
For an alternative browser, I really do use lynx. In fact regularly on my eeepc 1000. If you really want graphical, I do like netsurf.
This is true that some 486 based devices can be still found in the industry as control boards for some kind of machinery. But I do not expect them to get regular OS updates. IMO those boards sit in well protected LAN isolated from any external access and stuck with one kernel version, usually the custom one with which the machine has been bought. Maybe some updates provided by the manufacturer in case of any critical issues with machinery itself, no more. I would expect any modern machinery control boards implemented with some ARM-based SoC which integrates everything in one chip except a coffee machine ;p There are plenty of ARM SoC manufacturers nowadays and Linux kernel support is much better for ARM than it was decade ago.
In context of a graphical web browser I would look for something other than Firefox when it is heavy for RAM and not only that. That is why I asked for any alternatives you know about. The key here is JavaScript support, CSS, SSL etc. And this damn SSEx requirement ... All we need here is to be able to browse 'static' web pages when even i686 based machine will struggle to handle any modern multimedia web page.
