NXT Line Follower
The robot measures line position with the 4 line sensors and feeds this to a PD-regulator which in turn produces the two motor outputs. This setup gives a smooth line following.
The cost of the robot is roughly the cost of a set of MINDSTORMS NXT + 3 additional NXT light sensors and the rechargeable battery.
The time to build includes several mutations of the basic design - time flies when you play with LEGO ;-). Of course some time was spent finding some usable values for the P and D constants for the PD-regulation.
I used the Bricxcc IDE for developing the controller program.