This is the question on the minds of some commenters, some emailers, and a lot of people who don't read this blog, including a friend's father.
The answer is that most of you can relax. Your insurance policy and/or annuity will probably be fine.
The part of AIG that is insolvent is a holding company, which owns a bunch of subsidiaries--approximately one squillion at last count. The subsidiaries issue your life insurance policy, or the annuity you purchased for retirement. Those subsidiaries are mostly regulated by the states, which ensure that they have adequate capital to pay off their claims. That capital can't be tapped by the parent--though the State of New York, for some reason that I cannot fathom, is apparently prepared to let AIG take out a $20 billion loan from its New York subsidiary.
Of course, with markets in the state they're in, you may be asking yourself how long that capital will remain adequate. The good news is that each state has a guaranty company, which pays off the claims of insolvent insurance firms, at least up to a cap. That cap varies by state, but in no state is it lower than $100,000. Check your policy to find out what state it was issued in (I'm told it's not necessarily the state you live in, particularly if it's an annuity), and use google to find out what the guaranty cap is.
People with insurance policies or annuities with AIG can redeem those policies for the cash value of the policy, either with the company or with the guaranty institution. If I had my homeowner's insurance with AIG, I'd probably bite the bullet and buy a new policy elsewhere; ditto some massive asset. But in general, unless you're insured/annuitized for a huge amount and planning to die/retire in the next few months, don't worry. With the exception of wealthy folks who bought gigantic policies, you should be able to get at least most of your money back out.