What Gringotts vault once held the philosopher's stone?

Answer 1

Vault 713.

It was broken into on the 31st July 1991 (Harry's 11th birthday) by Professor Quirrell and Lord Voldemort. However as this was after Hagrid had emptied the vault the theft was unsuccessful.

Answer 2

The philosopher's stone was in vault 713.

On the 31st July 1991, Rubeus Hagrid removed the philosopher's stone from Gringotts so it could be taken to Hogwarts where it would be protected. Hours later, Lord Voldemort and Professor Quirrell broke into the vault attempting to steal with stone. They were, of course, unsuccessful and thus Voldemort decided he needed to be close to Quirrell and began sharing his body.

Vault 713 is a high security vault and as such is not accessed with a key, but by a Gringotts goblin passing his finger around the length of the door. If anybody else attempted to do this, they would be sucked inside and trapped there. The vaults are not frequently checked to see if anybody is inside, Griphook told Harry that they checked once every ten years.

It is not known how Voldemort and Quirrell managed to get the vault open - possibly the same way Harry, Ron and Hermione did in 1998 when they used the imperius curse on a goblin.

The vault likely belonged to Nicolas Flamel, Albus Dumbledore or Hogwarts.