The first thing that came to my mind when I started micro-controller programming was to set an automatic room heating cum humidifier system. Bangalore has a very confusing weather - especially for new-comers. The temperature is generally moderate, but nights can sometimes become very cold. However, on other days, the nights are warm and if you have a heater on - it becomes uncomfortable. Also, since the weather is generally moderate - automatic heating solutions are not available commercially.
Hence, one of the first projects I made on an arduino was a temperature and humidity controller.
Instructions for creating and using a "standalone arduino" can be found at http://dushyant.ahuja.ws/2013/10/standalone-arduin...