It is possible to have just the kernel and just what you want to run hardwired as the init process, say some minimal web server. A slightly more sane solution is to have a minimal init process that can respawn your server if it crashes.
As for filesystems, there needs to be something, I don't think it can work at all without a root file system, but a ram disk will do fine. The FHS directory structure isn't needed at all of course.
I've seen some ridiculously stripped down embedded Linux systems. Most tend to have something like Busybox though, with a fairly conventional look, but some prefer to just use that while developing and rip it out in the deployed version.
As for filesystems, there needs to be something, I don't think it can work at all without a root file system, but a ram disk will do fine. The FHS directory structure isn't needed at all of course.
I've seen some ridiculously stripped down embedded Linux systems. Most tend to have something like Busybox though, with a fairly conventional look, but some prefer to just use that while developing and rip it out in the deployed version.