Usually, we think of a pension lasting for the duration of a person's retirement (i.e. the remainder of his/her life). With annuities, you have more options available than that.
To learn what features are common to most or all types of annuity pension, see the page on annuity pensions in general.
A life annuity is the type of annuity most people understand. Your pension continues paying from the day you trigger it until your death.
The risk inherent in life annuities is that you might die early (maybe even before you trigger your pension). In a way, that's a good thing: the purpose of annuities is insurance against the financial hazard of living too long. From that point of view, life annuities offer great security. From another point of view, however, you took a sum of money out of your estate for nothing.
A period certain annuity provides an income payment every month for a fixed number of years. If the annuitant dies before the pension expires (or before it even begins), the pension pays to the annuitant's heir(s).
The danger of period certain annuities is that you might live much longer than you expected an therefore can run out of income. That's the very nature of the hazard of having no pension at all, isn't it? However, the purchaser of a period certain annuity has the security of knowing that his investment will have some return at least, which is not guaranteed by a life annuity.
A period certain option (different from a period certain annuity) creates a hybrid between life annuities and period certain annuities. A life annuity with a period certain option will pay either until the end of the annuitant's life or for a certain period, whichever is longer.
Cash refund annuities are another variation on the standard life annuity. They guarantee an income until the annuitant's death, but if at the time of death the total pension issued is less than the cost basis (how much the owner paid into the annuity during its accumulation phase), then the difference is refunded to the annuitant's estate.
Similar to cash refund annuities, installment refund annuities issue a refund in the event that the annuitant dies before receiving a pension at least equal to the cost of the annuity. Whereas cash refund annuities issue a refund as a lump sum, however, the refund from a life annuity with an installment refund option is issued in a series of payments.
Annuities with a joint-and-survivor option have two annuitants; your pension doesn't cease until both of them are dead. Joint-and-survivor annuities are designed for married couples, to ensure that the needed income is available even in the event that one dies long before the other.
You might well expect that if one of the spouses dies, the remaining spouse could get by on a smaller pension, and joint-and-survivor annuities can accommodate that. You can cut the cost of your annuity if you buy one which pays a lower pension following the first death.