Do these happen randomly or do you have to be low health. Example, sometimes a dragon will bite the dragonborn, and toss him to instant death. Was that because I was low health or can it happen at any time?

If it can happen at any time, then it would make no sense to fight a dragon in melee range unless you had a follower and/or conjured friends to draw attention, right?

you mean the kill-cams?

i believe they will only happen when the attack does enough damage to one-shot you (however, I don't think it takes armor rating into account)

With SkyRe, it definitely happens whenever the opponent has the opportunity to one shot, regardless of health.

I was always wary around two handers...but then I discovered the absolute screaming terror that is a enemy with a blunt weapon.

I don't know exactly how the game calculates these critical hits (or kill cam finishes) on the player character, however, I think having low health (or low total health points) does increase the chances of them happening (at least from my experience). How tough an enemy is compared to your character may also play some role in this too, since I seem experience them more on enemies that are at a significantly higher level than I am.