If you're looking for some simple, but interesting, circuits to build with your Arduino, the SparkFun Inventors' Kit is an easy, cost-effective option. This kit includes everything you need to build 16 different circuits - and I mean everything, including an Arduino, a breadboard, and a wide assortment of electronic components (LEDs, switches, sensors, motors, etc - they even include a screwdriver). If you've already got many of these components, they make it super easy to order any missing pieces from their web-linked materials list. I especially like the black backer board that holds the Arduino and breadboard in close proximity so jumper wires stay securely in place.
Another great thing that SparkFun does is publish all their tutorials for the 16 circuits online. At first I was tempted to skip around and try out only those activities that were new to me (after all, I can't tell you the number of times I've lit up an LED), but I stuck with doing the activities in order. Good thing. These tutorials are a great teaching tool, not just in electronics, but in Arduino programming. Each activity gets progressively more advanced building on previous concepts and introducing new ones. The tutorials also address real-world applications and suggest interesting variations to try out.
My only complaint with these tutorials was with the hook-up tables (which SparkFun actually stopped using after the third activity). The hook-up table in the first activity told me to put the LED in C2, but there is no C2 pin on an Arduino. It finally dawned on me that C2 was referring to the breadboard hole, not the Arduino pin. If you're like me, I usually just put my components into the first available breadboard hole and don't really worry about row and column referencing. I think a nice labeled diagram would be a much better substitute for this table. But to SparkFun's credit, they put a wealth of information into the comment sections of their sample sketches, so I've learned to skip straight to the comments when wiring up my circuits.
