How many prisoners were freed by the storming of the Bastille?

Actually, only seven. In France, 14th July, Bastille Day, is a national holiday and a glorious national symbol, equivalent to 4th July in the United States of America. From the rousing paintings of the scene, you might think hundreds of proud revolutionaries flooded into streets waving tricolours. In fact, only just over half a dozen people were being held at the time of the siege.The Bastille was stormed on 14th July 1789. Shortly afterwards ghoulish engravings of prisoners languishing in chains next to skeletons went on sale in the streets of Paris, forming the popular impression of the conditions there ever since.

Storming of Bastille fortress 

The thirteenth-century fortress had been a jail for centuries; by the time of Louis XVI it mainly housed people arrested on the orders of the king or his ministers for offences like conspiracy and subversion. Distinguished former inmates included Voltaire, who wrote "Oedipus" there in 1718.
The seven prisoners in in residence that day were: four forgers, the Comte de Solanges (inside for 'a sexual misdemeanour') and two lunatics (one of them was an English or Irish man named Major Whyte who sported a waist-length beard and thought he was Julius Caesar). Marquis de Sade was transferred from the prison only ten days earlier.

Prisoners in the rue Saint-Antoine after release from the Bastille on the 14th July 1789.

One hundred lives were lost in the attack, including that of the governor, whose head was carried through Paris on a pike. The prison guard were a contingent of invalides - soldiers invalided out of regular service - and conditions were fairly comfortable for most inmates, with relaxed visiting hours and furnished lodgings.
The cost of maintaining the Bastille fortress and garrison for so limited a purpose had led to a consideration of closing it, just shortly before the revolution began. It was, anyway, a symbol of royal tyranny.
The painter Jean Fragonard's sketch of visiting day in 1785 shows fashionable ladies promenading around the courtyard with the prisoners, who were given a generous spending allowance, plenty of tobacco and alcohol, and were allowed to keep pets.

Bastille's interior on Fragonard's sketch

Jean François Marmontel, an inmate from 1759 to 1760, wrote: "The wine was not excellent, but was passable. No dessert: it was necessary to be deprived of something. On the whole i found that one dined very well in prison." But, to be honest, his captivity was rather short - it lasted only twelve days.
Louis XVI's diary for the day of storming of the Bastille reads - "Rien" (Nothing). He was refferering to the bag in that day's hunt.

source: The History Notes