There are plenty of starter kits to choose from if you're interested in tinkering with electronics, but the Discovering Arduino DIY Kit is one of the more expansive. It gets you started both with general electronics and Arduino programming.
The kit includes over 130 parts as well as an Arduino UNO. Also included is a set of online instructions that guide you through a lot of different projects, ranging from regular old electronics tinkering to programming the Arduino. It's a nice, all-inclusive kit that doesn't just concentrate on the Arduino, which means it's a good place to start for anyone interested in tinkering with electronics.
Discovering Arduino DIY Kit ($79.99) [ThinkGeek]