An annuity is an insurance company product. An individual gives money to an insurance company that promises to make payments over some stated period of time and under certain conditions.
A good explanation of the different types of annuities is at www.answers.com, keyword "annuity". Annuity price quotes without having to enter personal data and suffer through numerous telephone calls from salespeople are available at www.immediateannuities.com.
The big risk to the annuity purchaser is that the insurance company will not be able to fulfill its promises. Insurance companies do fail. In 1999, A.M. Best published their research into the failures from 1969-1998 of 640 U.S. insurance companies. Of the 640 failures, they were unable to determine the primary cause of failure in 214 of the cases. Of the remaining 426 failures, the primary cause was "insufficient reserves" (145), followed by "rapid growth (underpricing)" (86), "alleged fraud" (44), "overstated assets" (39), "catastrophe losses" (36), "significant change in business" (28), "impaired affiliate" (26), and "reinsurance failure" (22). Insurance companies don't publicize this risk of failure. One large insurance company has only this one sentence deep inside the fine print: "Any guarantees under annuities issued by TIAA are subject to TIAA's claims-paying ability". In plain language this means: "If we run out of money for any reason, we won't be able to give you any".
One interesting aspect of the annuity industry is their terminology. Whenever they give you any money - even your own - they call it "income". Suppose you put $100 in a savings account at the local bank and one year later you close the account and receive $103. The bank says you have income of $3. The annuity industry says you have income of $103.
All this can be illustrated by a simple example. Immediate Annuities is currently offering a 5 year period certain annuity; you receive payments for 60 months and your beneficiaries will get this payment if you die within the 60 months. If you invest $100,000, your "monthly income" is $1,770. So in 60 months you will receive $106,200 in "income". This is a rate of return of about 2.39% per year. In contrast, Bankrate.com shows a five year FDIC insured certificate of deposit yielding 5.23% - at the end of five years you get back $129,032, an extra $22,832 more than the annuity. If you want to withdraw monthly from the CD, you can withdraw $1,898 per month, not the $1,770 that the annuity would pay. If you withdraw $1,770 per month from the CD, you will have an extra $8,734 at the end of the five year term. In simple terms, choosing the $100,000 five year annuity over the five year monthly withdrawal CD puts all your money at risk and takes $8,734 out of your pocket and gives it to the insurance company.
Would you rather invest $100,000 in a 60 month FDIC insured bank CD with an APR of 5.23% and "monthly income" of $484 or would you prefer to invest $100,000 in a 60 month uninsured annuity with an APR of 2.39% and "monthly income" of $1,770? If you chose the latter, start at the top and read this piece again.
There may be situations where an annuity is appropriate; but I don't know any. There is nothing that the insurance company can do for you inside an annuity that you can't do for yourself outside an annuity - and outside the annuity you save the 2 or 3 points per year (2.84 points in the example above) that the insurance company charges you and you also avoid the risk of insurance company failure.
What, after all, is the value of FDIC insurance to you? Suppose you go down to your local bank to get a 5 year CD and they offer you two products; the first is 5.23% CD backed by the FDIC and the second is a CD not backed by the FDIC. Your friendly banker tells you that with the second product you might lose all your money. How much more yield would you demand to take this risk?
Is this really a risk you want to take at any price? For me the answer is "no". I would not touch an annuity (or any other product where I might lose all my money) with a ten foot pole even if it was someone else's pole.