I've noticed that if you check the Libra screen for monsters, it says their taming status (either 'tamed', 'tameable', or 'untameable'). I have yet to see a common enemy that isn't tameable so I haven't really been paying any mind to this.
I'm assuming that it's ONLY bosses and other storyline-related enemies that aren't tameable but I figured it's worth asking. Is EVERY random encounter enemy in the game tameable? If not, which aren't?