I've got a machine running Linux in my study. It's my previous desktop machine, now relegated to Linux tinkering box and fileserver. It's never switched off, hasn't crashed or misbehaved since I set it up, and works flawlessly.
It runs Fedora core 5, which seems to be totally stable - certainly far more stable and reliable than Windows on the main PC - and a lot faster, too.
It does have a keyboard and a (very old LCD) monitor, although the monitor is usually in standby mode and blank.
Linux is a bit harder to set up than Windows (or was for me, anyway, although there are those who will tell you I did it all wrong). Once done, it's excellent.