There are many Internet-connected Arduino methods that can be used to scrape the weather forecast from various services, however this version by Japanese Arduino and electronics enthusiast Ken Kawamoto has to be the best so far. His system gets the weather forecast and then physically simulates the weather inside a small container. So if it's going to rain - a water pump creates rain, or ultrasonic diffuser creates mist for fog, etc. Add some RGB LEDs and you can have sunshine - it's amazing:
If you need to create a larger, Internet-connected Arduino project - there's only one board to use - 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.