There's never really been a need to change it since it's stable and handles all our needs.
Personally, I would be slightly worried to have a 10 years old machine as a single point of failure for a service as important as internet connectivity. Your priorities might vary of course, but a PC's life frame typically ends after 5-7 years. Mechanics (fans, HDD) are a likely candidate for a failure, although the electronics will show signs of "wear" too (electrolytic capacitors used in voltage converters all around the device might dry out over time, plug-in contacts would oxidize resulting in raising transition resistance, similar effects might be observable on low-quality soldering points).
Not much will be won in terms of either performance or reliability by replacing the NICs, although routing latency theoretically would benefit slightly due to shorter bit-times of Gigabit networks. The effect would be negligible however, as a receive-send cycle of a 512 Byte FE frame amounts to roughly 0.01 ms while average host latency is larger by the order of a magnitude at approximately 0.5 ms.
BTW: if you are looking for a cost-effective replacement and are comfortable with Linux, have a look at OpenWRT. It runs on a variety of embedded commodity hardware and allows for redundant setups. The faster MIPS- or ARM-based models (>=500 MHz CPU, >=64 MB RAM) perform rather well and would be able to do wirespeed routing (and probably also filtering, but this would depend on your ruleset) for 100 Mbps interfaces.
You would likely save the device's purchase price worth on electricity after 1 year of operation (assuming 100 W of power for your current setup and 10 W for an embedded setup you would save roughly 2 kWh each day which amounts to $100 each year at 0.15 $ per kWh).