Arduino enthusiast Jean-Francois Lagarde has published a detailed description of how to make his open-source weather station based around an Internet-connected Arduino board. The system measures humidity, wind speed and direction, temperature and humidity. The data is then passed over to cosm via the Internet for remote monitoring and analysis. It is true that weather stations aren't anything new - however the level of documentation for this project puts it in the "outstanding" category.
When building larger Arduino Ethernet-enabled projects - it's time to upgrade to the Freetronics EtherMega:
Quite simple the EtherMega is the fully-loaded Arduino-compatible board on the market today. Apart from being completely Arduino Mega2560-compatible, it includes full Ethernet interface, a microSD card socket, full USB interface, optional Power-over-Ethernet support and still has a circuit prototyping area with extra I2C interface pins. So if your project is breaking the limits, upgrade to the EtherMega today.