Is there really an advantage to sifting flour that I bought that was labeled 'sifted'?
Flour is unusually variable in how densely it will settle, so this can make a big difference for some recipes. The purpose of sifting is to make the amount of flour in a given volume reliable. (If you are measuring by weight, you don't need to sift.)
By moving around the sifted flour, or pouring it from one container into another, you are changing the way it is packed. Therefore, you can easily "unsift" it in the course of normal handling. Proper sifting is done straight into the measuring device.
Assuming you're baking: Sifting does more than just standardize the density of your flour (which it doesn't even do all that well). Most recipes that call for sifted flour do so because it helps aerate the batter, as well as keeping the flour from clumping and forming lumps. It won't incorporate a large volume of air, but it will bring in lots of microscopic "seed bubbles", which will then provide lots of nucleation points for the leavening to form CO2 bubbles. Without those seed bubbles, you'll get fewer, larger bubbles of leavening, resulting in a different texture. (Creaming sugar into softened butter performs a similar function in many recipes.)
Also, +1 for hobodave's food processor tip. Or a good whisking in a large bowl will do in a pinch.
It can't hurt. I wouldn't trust flour that came pre-sifted. Anything will settle during transport.
Random tip: pulse your dry ingredients in a food processor instead of sifting.
Also by sifting flour ensures no foreign objects are in the flour...bugs, toys, coins, large flour lumps, chocolate chips, cupcake sprinkles, pet fur, etc.
If you have small children that help you bake, or pet friendly kitchens, you'll be surprised what you can find in your baking ingredients!!
Bugs sound gross but they do happen, especially in old house kitchens, or if you use a tub or other container to hold your flour, better to find out if you have a problem before you start mixing!
Ideally your recipe will have the flour by weight, not volume, as you can't reliably tell how much flour you are adding when you measure the flour by volume. You should search for baking recipes on the net that list the flour by weight (good books do this for bread baking; the Bread Bakers Apprentice does this, for example).
After weighing the flour you should still sift it as this adds air and can help lend lightness to a quick bread or cake.