My personal opinion is to never buy them.
They generally have higher costs than regular mutual funds. An insurance salesman will earn a big commission from selling variable annuities, at a disadvantage to you. Although the tax free compounding is nice, there are other ways to avoid tax, even if your tax shelters are full.
I think a tax managed growth index fund can have a pretty low tax profile. The index fund has the advantage at eventual withdrawal the lower tax of capital gains, compared with the higher tax of annuity income withdrawal.
The step up basis adjustment of an index fund is pretty attractive to your heirs when you die. ^^;;
If you need insurance, buy a term life insurance. What if you are too old to get one? Well, your savings are supposed to carry you after a certain point.