* Day of the week: Weekdays see significantly more car usage than weekends.
* Time of year: Driving habits change with seasons and holidays.
* Region of the world: Car ownership and usage differ dramatically between developed and developing countries.
* Definition of "driven": Does this mean a car driven for even a short trip, or only longer commutes?
To get an estimate, one would need to aggregate data from many different sources worldwide, which is a massive undertaking and doesn't consistently exist in a readily compiled form. Any number you find would be an approximation with a large margin of error.