My first Arduino experience was with Adafruit's Boarduino back in 2008. I don't know why I went with an alternative to the original, but I think it was because I already had rockets in mind and the boarduino's form factor was perfect. It was a bit of learning curve, but I was amazed at what could be done. Blinking LEDs!
Fast forward five years, and I've got a number of projects under my belt, and am part of an Arduino group at work. Here are the slides from a presentation I gave called The Cult of Arduino. A number of advances in microcontrollers have been made, but the open-source hardware and software model of Arduino has kept them in the forefront. Linux and ARM are the buzz-tech of the day, but if you want to get down to bare metal and flash LEDs using an 8-bit real-time operating system, Arduino will get you there.
If you are wondering what you could do with an Arduino, check out a couple of easy and cool projects from Sylvia: