Probably one of most common projects among embedded starters is Larson scanner. It is basically a row of LEDs that runs lights with fading effect like Cylons eyes from Battlestar Galactica or KITT Knight Rider movies. If your next project is gonna be Larson scanner you may want to check out this thorough tutorial that may save you some time.
Tutorial is based on AVR Atmega168 microcontroller. Circuit is really simple for this 8 LEDs with current limiting resistors and ISP header for programming. In particular case you can program Arduino board directly for this. Program is written in C and all parts of it is well commented. Basically there is no wonder – only PWM play.