I've only killed random characters I've run into out in the wild: The nameless mercenaries, after they tell me where they're headed; the imperial couriers (they always have bad luck with me, anyway. One showed up to apparently give me a message at the College of Winterhold -- pure Anti-Imperial territory, and I followed him as he ran all the way out and around a mountain, away from Stormcloak arrows, before finally getting blindsided by a Snowy Sabre Cat. Poor bastard, just when he thought he'd reached safety), and the occasional thief and his pursuing guard.
The only named character I've killed when I didn't need to was that one bard from Riverwood, when I needed a sacrifice for a particular Daedric quest.
I've Fus Ro Dahed my wife to death a few times in my house - I just always save it before so I can go back. Love the ragdoll physics.
I've killed the Warmaidens owner's wife in Whiterun (forget the name). She was the unfortunate victim of me vs a lot of guards one night. Now the guy who owns the shop always complains to me about how hard things are without her there. On the bright side, I never have to kick her off the grindstone, forge, or tanning rack when I need to use them.
When someone sends thugs after me for stealing from them, I make it a point to go back and kill them. Just killed Brina in Winterhold last night for doing that.
If you love the ragdoll physics, you should go to Mistveil Keep in Riften and use that shout just after you enter the front door. Good times, good times.
I have yet to kill someone just for the sake of killing them. I'll save that for my psychotic evil character i create one day. Right now it would be too vulgar a display of power.
You just found your character for it, too: The Cowboy from Hell.