How many key characters are too many to kill off in a novel?

George RR Martin has shown, with A Song of Ice and Fire, that you can kill half your cast, good people as well as bad, and then go on and still tell a compelling tale. Tolkien killed only one likeable major character, and then unkilled him in the next volume.

In Empire, I killed my protagonist, very abruptly and shockingly. But I already had two other good viewpoint characters, so I didn't leave the readers stranded.

What you need to avoid is the sense of betrayal in your readers. GRR Martin flirted with this with the characters Robb and Ned -- we had the expectation that their stories were going to be the main thoroughfares of the novel, and suddenly they were gone, and therefore had no future in the tale. How did he compensate? By making us care more about other characters, like Tyrion Lannister, so that outcomes still mattered to us. He also made us care about characters we didn't like at all, like Cersei. And he could give beloved characters crippling injuries, which they have to cope with from then on.

When have you killed off too many characters?

If there's no one left that we already liked or admired. You can't run the car very long on just fumes.

When there's no reason to suppose that the important issues will be resolved satisfactorily.

When the deaths become a joke, like redshirted characters in Star Trek.

When you have no viewpoint character left.