I voted for "uncommon, but the threat is always there".
Well, I'm sure there are, but it's kind of a Maslow's Pyramid thing. If you don't feel safe, you'll seek safety until you do, at the expense of other less important things. Adventuring isn't safe, and adventurers shouldn't behave as if they are in no danger when they fight mythical monsters on a regular basis.Aren't there are things the PCs care about besides their personal health?
No. There are plenty of other games one can use to tell stories. In D&D, death happens when it happens. Sometimes due to certain circumstances and other times due to rotten luck.
It's pretty obvious that in the oldest campaigns, past a certain low level, character death just meant "Dammit, now I have to sell some of my magic items to pay for that raise dead spell." Death was just a way for the DM to part the characters from their wealth.
Death's frequency should be determined by how dangerous the opponents are.
If the DM and players don't want characters to die, they should attempt to resolve encounters without entering into combat -- sneaking, diplomacy, bribery, running away, etc.
I think it's incumbent upon DMs not to force the characters into combat with every encounter. Opponents don't want to die as much as the characters don't want to die.