If you're talking about the carbon in filter cartridges, I don't bother replacing it.
However, I do make my own carbon filters for my tank using pantyhose and a cheap tub of activated carbon from the store. It's a good way to remove any harmful chemicals from the water that water conditioner doesn't take care of. It also acts as a second line of defense against chlorine and chloramines, and helps to remove the smell from the water.
While carbon isn't needed, per se, it's an added bonus to your aquarium. I choose to use carbon since it's relative cheap. A big tub of it costs about $7 and lasts almost a year.