The lifespan of carbon is determined by its binding capacity (i.e. the amount of carbon you have and it's usable surface area) and the organic and inorganic load in your tank that will be bound by the carbon.
Carbon can last a few days in a poorly filtered and poorly maintained aquarium, or it can last months in a well filtered and well maintained aquarium.
Many people don't even use carbon. They feel that if you have a well maintained aquarium, then there is no need for carbon, and that space in the filter could be used for more mechanical, biological, or some other filtration. I agree with this, but I personally have much excessive biological and mechanical filtration as it is, so I use a SeaChem Matrix Carbon and SeaChem Purigen combination in one of my canister filters to make my water that much more crystal clear. I replace the carbon every 6 months during my biannual filter cleaning.
If you are looking for carbon, I'd suggest SeaChem Matrix Carbon. This is the best carbon out there.