If an insurance company is having financial problems, you don't necessarily have to pull your money out of the annuity. Even in a financial meltdown, there's no need to sweat when it comes to the safety of your annuity and the stability of the insurance company behind it. First off, if the annuity is a variable annuity, the present value of the separate account (investment portion) would be covered up to $500,000 under Securities Investor Protection Corporation (SIPC) regulations. This is similar to the FDIC coverage at bank accounts, but investment accounts are covered by SIPC.
However, if your annuity is not a variable annuity held in a segregated account, your annuity would likely be covered by a state guaranty fund. States typically cover annuity values up to $300,000 for life insurance death benefits, $100,000 in annuity withdrawal and cash value, and $100,000 in surrender values for life insurance. So check your state guaranty fund's coverage limits to see how much of your annuity will be covered, and if it covers the whole amount you wouldn't necessarily need to cash out to avoid losses. If your annuity value exceeds the covered limits, you may need to weigh the taxes and penalties of taking your money out and make a decision from there, or consult a professional.
Next, keep in mind that insurance companies have recurring annual fees (profits from mortality, administrative and operating expenses) that are collected from your annuity each year, which makes annuity business typically one of the insurance company's more profitable lines of business. Because of the recurring revenue stream, it also makes the annuity sector very attractive to other insurance companies as a "buy-out" piece if your insurance company happens to go under.
This question was answered by Steven Merkel.