I have a Samsung Galaxy S4 here which is about a couple of months old running on its stock iteration of the Android OS (4.4, "Kitkat"). After charging the phone it just sits there on standby after which, suddenly, it rebooted itself and then posts to Recovery mode. To be honest, that really flipped me out (as I was home alone at that time, really spooked me).
Am I missing something here? Is the phone's operating system corrupted or something? I let it drain the battery and never touched it until I can come up with an explanation and, so far, Google's not helping.
If you're using stock recovery there should be no worries (emphasis on "should"). Just try rebooting the phone and if it seems to not be doing something as it should, just boot back into recovery and hit factory reset.
If that doesn't work you'll have to find a restore image (which is a major pain and time consumer) to flash with odin.
Is the phone rooted? I used to have a S3 that rebooted into recovery whenever I wanted to take a system update. It usually isn't possible to update stock firmware with root enabled. You might have automatic updates enabled.