One of the first projects I took on was using the Pi to make a full time weather station go live online in my backyard. The station itself is just a kit that is available to purchase online. It came with a temperature and humidity gauge, a rain gauge, a wind vane (direction), and anemometer (wind speed). It normally feeds data wirelessly to the console shown below that would be viewed at it's location in your home. It also comes with software to view the data and upload it online but that would require a big full computer running 24/7 and wouldn't be a very green or efficient use of a computer.
The Pi is a perfect solution to this because it can run on it's own without a keyboard, mouse, monitor, etc. and running 24 hours a day, 7 days a week, 365 days a year it will use approximately $5 of electricity. The panel shown above hooks into the Pi via USB and the Pi grabs the data from the stored memory every 10 minutes. It's then uploaded to the weather site of choice Weather Underground. You can see a screenshot of a the log as it collects the data.
The weewx software uploads the data to Weather Underground and can even create it's own HTML page of charts and graphs you can FTP to your own website. To me, the WU site works just as well as I can use the site or the app to get the information straight from my backyard!! At the bottom of this page you can see the "badge" from my station with the current stats. There is a lot more data on the webpage itself for my station.
As a side note the same Pi also pulls double duty as a print server for my entire house. The printer is connected to directly to the Pi and then shared with every computer on the network. So that means with out another computer running (well not really anyhow) I can print from any machine in the house and again not have another full machine running all the time.