Carl from the Arduino forum has designed and built an outstanding ultrasonic anemometer (to measure wind speed and direction), and after reading the description and details - is an outstanding example is what's possible with the Arduino development environment. The wind speed and direction data can be logged for analysis and monitoring, and Carl has included not only the Arduino sketches for operation and calibration but Visual Basic code for PC interaction.
If you're looking to work with your own weather-sensing equipment, but don't want to make your own devices - it is possible to interface Arduino-hardware with existing commercially-available weather stations. The key is to capture the wireless data from the sensor and interpret this with an Arduino. Many people have done this with out 315/433 MHz receiver shields:
Apart from being idea for working with the various low-cost data links on the market, the shield can also be used to capture wireless weather station data, as described in the book "Practical Arduino". For more information and ideas, check out the product page.