I've done some experiments with low-cost robotics platforms.  I found that Tamiya have cheap kits which are good for this, namely the "Wall Hugging Mouse" kit and the "ShovelDozer" if you need dozer-type traction!  I modified the wall hugging mouse, adding larger model airplane wheels to allow it to operate on carpet, and gutting the "electronics" (if you can call a single microswitch "electronics"), replacing it with a PIC 16C84 microcontroller, L293D H-Bridge DC Motor driver chip (actually 2 piggy-backed to supply the needed current).  A basic TTL oscillator running at 40KHz drives 2 near-infrared LEDs and is controlled by the micro.  The micro reads a Sharp infrared remote-control sensor to see if any objects have bounced any of the infrared light back, thus forming a "radar" object detection scheme.  The microcontroller then switches the motors accordingly.  The rest of the smarts are in the software.
One day, I'll get around to putting the circuit details on here.
Email me if you want them.
Side view of a modified Tamiya wall hugging mouse.  Top right is the Sharp infrared sensor atop the batteries (1x 9V and 4x AA)
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c 2004 Greg Newton
The Tamiya Bulldozer kit has good traction, can drive over things almost it's own height, and has plenty of room on the chassis for control electronics etc..  It comes with the dual motor and gearbox set.  Did I mention it was cheap!
I found a single L293D got very hot so I piggy backed 2 of them to double the current handling and soldered a heatsink across the 2 centre ground pins on each side. I got the heat fins from an old audio amp chip, but any old aluminium cut to shape will do.