Running a process at startup and viewing its console output via ssh (or other means)

Is there a way I can have a process on a headless server which runs at startup, and still be able to connect remotely at a later time to view the console input? I need to be able to view console output via ssh or some other means. Simply redirecting output to a file won't work because these processes never exit and constantly output lines. If I just redirect to a file it'll fill up the disk... (I only really care about the last 20 lines or so.) I don't think "screen" is an option since I need run at boot time without interaction.