If you have an older annuity- you may want to get familiar with a 1035 exchange. 

The 1035 exchange refers to the section of tax code that allows investors the flexibility to exchange one annuity for another without incurring any immediate tax liabilities.  It makes sense if you have annuities with high fees or poor investment choices/interest rates. 

CNNMoney provides some basics on "non-qualified" annuities.

You do not want to cash out your existing annuity and then reinvest in a new one. That would trigger tax payments and a 10 percent tax penalty if you do so before age 59 1/2. Instead, you want to do a "1035 tax-free exchange," which is the way to move your money directly from one annuity to another without creating a tax bill. The company you're getting your new annuity from can fill you in on how to do this maneuver.

One caveat, though: before you do a 1035 exchange, make sure the annuity you're going into doesn't have surrender charges that will make an early exit costly.