Annuities can be one of the most expensive ways to invest your capital. Remember they are insurance products.
Variable annuities can often times run into the low-to-mid 3% range in annual fees. These higher fees can prohibit growth. Make sure you are willing to pay for the insurance part of this type of product before purchasing.
Almost all annuities are non-liquid meaning you may have difficulty taking all of your money back should you change your mind.
This is due to most annuities having lengthy surrender periods, or a penalty for withdrawing all of your funds before a certain time period has lapsed. These can range between 5 - 12 years depending on carrier and product.
The only thing guaranteed in life is death and taxes. Annuities are no different. While they do have a "guaranteed" aspect to them, that guarantee is only as good as the insurance company issuing the policy.
While insurance company defaults don't happen often, defaults can certainly occur. It's important to choose a carrier with a strong history of financials. If it looks too good to be true, you should be asking more questions.
By their nature as insurance products, they may very well come with limited flexibility. Since these are insurance contracts, there are often times predetermined benefits that once started aren't easily changed.
Annuities with market exposure may also have fairly limited sub-account or index options for you to choose from. If flexibility is most important to you, then you may not be best served by utilizing one of these products.