Jayne,
The risk for a fixed annuity is relatively straightforward - as a fixed annuity holder, you investments are part of the general investments of the insurance company, so your risk is if the insurance company defaults/fails and is unable to pay back all of the fixed annuity holders.

The best way to evaluate this is to look at the financial ratings of the insurance company. Especially in today's difficult financial environment, stick with companies that have pretty high ratings from all the ratings companies (and the insurance company should be able to provide information on its ratings).

It's also worth noting that all states have an Insurance/Annuity Guaranty Fund, that will insure annuity owners in the event of a default for up to $100,000 of cash value (with higher limits in some states). However, this is not an excuse to avoid doing due diligence anyway to ensure you're working with a solid insurance company.

I hope that helps a little!