I think this is a key question for novelists and is really down to 3 things;
Depends on your genre; chic lit is unlikely to have any!
Depends on your readership; thrillers can range from the tame (single death) through to complete carnage (Game of Thrones) and your readers will give you a certain amount of artistic licence as long as you don't overstep their boundaries
Depends on the complexity of your plot; you will need a fairly large cast of characters if you are going to keep bumping them off in the name of your storyline.
I do think there is a correlation between the number of corpses you create and the darkness of your storyline. If it’s a really hostile universe in the fantasy genre, you can kill off nearly all of them, Aliens is a great example.
Traditional murder mysteries (Christie, Allingham, Marsh) usually have one or two murders, where the ensemble cast of characters all have a motive for bumping them off. The plot then is painting the puzzle of motive and opportunity.
When I finished Keeping Secrets I would have said it was fairly tame by some standards. Each death served a plot point or moved the story forward. I was shocked when one reviewer listed the body count at 7! I thought is was much less than that.
If a death does not move the story forward, does not contribute to the growth of other characters or the solution to the problem they face, then it’s unnecessary and people get tired of that sort of thing. (Unless they are fans of Mark Billingham)
Every time a character is on the chopping block, the writer needs to ensure it isn’t just for the shock factor, but actually contributes to the readers journey.
Tolerance of a high body count will also depend on the way the deaths are written. Lots of blood and gore may take a story close to the horror genre with lashings of blood and gore. For me it is important that the description should shock but not repulse the reader. I trust them and their imaginations to visualise the scene in a level of detail they are comfortable with. I don't need to describe every slash, cut or shot to achieve that, I just need to take them to their boundary and let them cross it if that is what they want to do.
There is another important factor to consider when writing deaths into a plot; does the victim deserve it or not? If the characters are written well a death may engender outrage, sorrow and loss if they are fundamentally a good/nice character. Conversely, some readers have a well developed sense of revenge and outrage. If a bad/evil character 'cops it' they may feel a degree of vindication or comeuppance. I certainly did when writing some scenes.
My deaths were spread out over several decades in different locations and connected by a single character who was instrumental in their lives and their deaths although who did not commit the deed every time.
I do have some self imposed rules for the characters I bump off;
No stereotypical deaths/violence of women/girls; there are people that write that stuff but it is not for me
Death is always significant and for a reason and has to be dealt with respectfully (even if it is a villain)
Death should deal with universal human emotions such as desperation, denial and revenge; emotions that readers can understand even if they don't agree with the outcome.
I write the death for the character and not the other way around. There is a lack of authenticity about characters that are written purely to raise the body count. I want readers invested in their longevity and who want them to get to the end of the story intact. It means more to them when they don't.
George R. R. Martin, author of the A Song of Ice and Fire series (Game of Thrones), is famous for the fact that any one of his characters – no matter how important – can die. He states:
I’ve been killing characters my entire career. Maybe I’m just a bloody-minded bastard, I don’t know, [but] when my characters are in danger, I want you to be afraid to turn the page [and to do that] you need to show right from the beginning that you’re playing for keeps.”
The unpredictability attached to Martin’s character deaths enlivens his stories. But being unpredictable doesn’t mean writing death scenes purely to shock or pull cheaply on heartstrings.
I am about a third of the way through writing the sequel to Keeping Secrets and I think the death count may be lower in book 2. But then I thought that about the first one.