I started with the sparkfun inventors kit and only did about half the projects.
I like to bounce from project to project.
I currently have a half done robot using the magician chassis http://www.sparkfun.com/products/10825
a 180deg scanning "head" using the kit supplied servo and a sharp medium range ir proximity sensor http://www.sparkfun.com/products/242 and a motor control shield that I put together based on a SN754410NE Quad H-Bridge Motor Driver
I also have another half done project which is an eddy current sensor.
I flick back and forth between the two as the mood takes me.
But the one thing that constantly lives on my arduino, and which I recommend as a good first project, is to build your own LCD shield. It's the easiest way to get your arduino communicating with you and it gets you started with soldering things which is something that you will need to be familiar with as all the really cool stuff will be DIY.
You can wire it up in standard fashion from parts or you can buy kits or you can go further and do things like wire it through a shift register to free up pins. It depends on how adventurous you are.
Another good project to put together (and it's really just software if you have the LCD shield) is the frequency measurer.