I agree with some what what both Zahir and Magnus have said.
I don't think that killing off a TV (because that's what I'll be talking about here) character is a bad thing, but like Zahir said, it could go either way. For me, it largely depends on what the reason behind the "offing" was, and whether or not it will resonate with the other characters in the show.
I do think it is rather formulaic in that when series need a jump, they kill someone, and the TV ads basically say "Oh look, one of these TEN people is going to die," and then it's up to you to guess and guess about it until it finally happens and you hate what happened. Let's look at some examples:
1. As Buzz said, Rescue Me kills someone at least every season. The death toll has been inching up and up each year, and I'm getting tired of it. They killed Tommy's son, his brother, his cousin (dead before the show started really) and left him and his cousin's widow (who he is dating) in a burning house at the end of last year. Do I expect someone to die? Maybe. But do I think they will? No. Why? Because Tommy is the star of the show, and Denis Leary, who plays him, is the creator and a writer for the show. That would be stupid. And the girl in the house is part of an on-going plotline involving several characters, so that won't happen.
2. ER premiered this year with HUGE buzz about the fact that someone was going to die. I swore up and down that if it were Abby I would hate the show because I really like her character. Was I worried? A little, but not much, because she is one of the MAIN characters of the show, and has a lot of story left to tell. Who ended up dying? Sam's ex-husband who I didn't, and I suspect many didn't, give a crap about in the first place. But this may present challenges for Sam and her son since she murdered the man. We'll see.
3. Nip/Tuck killed this blonde-headed nanny that Sean McNamara was cheating on his wife with. I really HATED this. Why? Because while I was shocked at her literal SUDDEN departure, I knew it was coming. I knew when she walked out in the street that SOMETHING was going to hit her. I was more shocked at how mangled she was than by the fact that she actually died. And why did I hate the death of this character? It wasn't because I liked her, but it was because in the following week's episode, it was completely forgotten about as if nothing ever happened, nobody was grieving or anything. Tsk tsk.
Those are three bad examples. A good example, I think, is Buffy the Vampire Slayer. With this show Joss Whedon only killed people off when it tied into a storyline and when it would resonate with the characters. I can't think of any character that died, that I cared about, that didn't affect the story somehow. Maybe Anya, but that's only because they didn't have time to show effects of her death because it was the last episode. Buffy, Tara, Joyce, Angel, Jenny, Kendra, and others I may have forgotten--all these characters who died had some sort of affect on at least one, if not all of the characters, and it wasn't simply thrown away.
MY POINT is that killing a character simply for shock value and to get viewers is something that I really HATE. I don't mind when characters are killed off as long as there is a good story to go along with it. If it's not tied in to a good story, then what is the point in doing it in the first place? You don't just haul off and have Barnabas walk out into the sunlight one morning and die, with no story supporting it.
So, if a new DS truly did need to kill off characters, great! Go ahead! I can live without some characters. I've done it before and I can do it again. You just have to get used to them being gone. But what I can't get used to, and what I can't accept is if the writers of this new DS were to just kill off Barnabas or Julia or Roger or David or Vicki or anyone just for the sake of saying "Hey, we're edgy, so throw some ratings our way!"
And, at the risk of making myself look like a fool and discrediting myself in this series post, I give you this: