Not sure MDF is quite the right material.

My robot (Cylon) has a plywood base which because of the laminated style of it probably has a bit more rigidity.

The motors are mounted using purpose made plastic mounts (Not sure the exact type but appears to be 13mm acrylic). This whole assembly also has a steel plate on the underside to provide further support.

The robot I have just bought (Hydra) has the whole arrangement made from 3mm aluminium.

The problem I would see with MDF is that as it is a manufactured fiberous board it has not got any inherant stregnth and could tend to break easily.

Im not that aware of what other people use so Im sure someone will be along in a moment to disagree with me.

Andy