The car used by Will Smith's character is a concept car called Audi RSQ, which was designed exclusively for the film and includes special features suggested by director Alex Proyas.
No re-shoots were required, a rarity for a movie as big as this.
For the character of Sonny the accused robot, the effects team used the same process that was used to create Gollum in the Lord of the Rings trilogy, with Alan Tudyk providing the body movements and voice for Sonny.
Will Smith told how he wrecked the motorcycle at around sixty miles per hour, during the filming of the scene at the robot storage facility (you can see him begin to lose control in the film).
The corporation in the movie is called "US Robotics." A company under that name exists in the real world too (presently "USR"). Both got the name from Isaac Asimov's works and its fictional company "US Robotics and mechanical men."