Arduino robot hacking is a great place to start.

An alternative or complementary approach is to work in simulation, and with that decision you can immediately start working with state of the art stuff, as follows:

ROS is the dominant Open Source robot platform. It works with the powerful Gazebo simulator. It's all free. Researchers, companies, universities, and hobbyists all use it, and there's an active community. The learning curve can be steep, but this is powerful stuff.

http://www.ros.org/

For a simpler start, take a look at the platform that was popular before ROS overtook it: Player/Stage

http://playerstage.org