What is the type of annuity in which all payments cease upon the death of the annuitant?

Typically that would be a "life only" single premium immediate annuity, meaning it pays a set payment to the annuitant until death, then it ends. It would be the highest payout option, but most people wouldn't choose this option unless they have no beneficiaries, or have used some of the payout to fund life insurance.

Most deferred annuities will have the "life only" option available as well, when a person decides to no longer defer, but wishes to annuitize their policy, they can choose "life only," "Period Certain," or "life w/period Certain"