The first problem with annuities is that you have to buy them from a salesman.
The worst problem with annuities is that when you do the math, you realize you're tying up your money for 10 years to get the same return you could get from a 3-year federally-insured CD. Don't be fooled by the fake "equivalent return" numbers they quote. The number to look at is the internal rate of return. It never even matches the inflation rate.
It's always been a mystery to me that no 100-year-old insurance company has the confidence in their investment team to write a contract that simply guarantees a reasonable fraction of historic stock market returns. They would clean up on the spread, and put the stock brokers out of business! Think of it -- they have the longevity to survive dips in the market (unlike us mere humans), they have the knowledge and experience to successfully play the market -- and they even get to keep what's left in your "account" when you die! So why aren't they willing to write a non-crooked contract that does something beyond just dribbling your own money back to you until you kick the bucket?
I guess the answer is they don't have to. There is an endless supply of marks who won't or can't do the math.
I would LOVE to buy an annuity and quit worrying about how to invest my money. So far, I've never found one that wasn't a scam.
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