It really depends on the built-in ethernet chipset being used and the drivers.
Most built-in ethernet chipsets from 3Com, Marvell, Intel, or those integrated into nVidia nForce chipsets use minimal CPU power as the chipsets offload much of the IP and ethernet functions.
Like sturm mentioned, if you have a recent machine, even a lesser chipset will have negligible impact on your CPU.
More likely, like Folken mentioned, it's *other* software like Anti-Virus software and software firewalls that eat more CPU cycles (AV software) or slow down the network to process/inspect each IP packet (software firewalls) via the CPU. Even these types of software have only a small impact on newer 2GHz+ computers.