The discussion can go anywhere people want to take it. What I specifically had in mind was actual on screen deaths, so a lot of the sci-fi shows where entire planets get wiped out weren’t what I was going for (but enormous in terms of body count). Hadn’t thought about Gunsmoke, that’s got to be a contender just based on longevity. I’d forgotten about 24 - even leaving out the nuke that’s got a pretty serious carnage rate. Still, on a per episode basis of people actually being shown getting killed, it’s going to be hard to top SOA.
“Revolution” had hundreds of deaths in every episode. If things had been that way in the whole 15 years since the lights went out, I couldn’t believe anyone would be remaining.
Quincy and Murder She Wrote had dead bodies every episode.
Why anyone ever invited Jessica Fletcher to a dinner party is a question that will never be answered. Someone (or more) was going to DIE!
Twelve O’Clock High would be a high one.
In murders per capita, I’d look at Cabot Cove, Maine, and Absaroka Co., Wyoming.
I don’t think Buffy approaches Gunsmoke levels, but between the deaths of the monster of the week and their victims I’m sure it’s several hundred on screen deaths.
ETA: It wasn’t called Buffy the Vampire Slayer for nothing. It had to earn it’s title.
Don’t forget Combat! starring Vic Morrow.
Sticking to earth, Sledgehammer blew up NY City with a nuke.
How many times has Doctor Who showed whole races being destroyed by the Doctor or one of his adversaries? And that show’s got 50 years of such a fine tradition.
Doctor Who was going to be my answer because it depicts the complete end of the universe with the complete extinction of all life everywhere. Can’t be any more deaths than that.
And the universe ends multiple times in that show. Although, then you have to ask if it counts as a death if the Doctor is able to recreate the planet and all the people in it, memories intact. Or does it count if he warps to he future and checks out a planetary graveyard. I mean, of course those people were going to die.
South Park, if Kenny’s deaths are each counted separately.
Highlander has got to be up there for on-screen deaths. An immortal gets beheaded in nearly every episode, and that’s not even counting the collateral damage of mortals.
Proportionally, I think the Blackadder series does. In several of the entries (not in all, I think) everybody dies. It’s worse than Hamlet.
Oooh, ooh, that reminds me: Dinosaurs, for the same reason.
He said he knew what he was doing! 
According to this site, The Rifleman showed 245 killings over 168 episodes. According to Wikipedia, Lucas McCain was responsible for 120 of them.
So, not the most by any stretch, but notable for the high rate at least.
A goodly number of her victims were, as you say, vampires, so they were already dead and shouldn’t count. What she was mostly doing was littering.
Probably the original Law & Order. It’s been on forever.
Edit: dang, **Quimby **beat me to it! 
What was the body count on The Sopranos?