How many animals total of each Kosher species were in the teivah during the flood?
According to Rabbeinu Bachyeh, 16 of each: 7 males for korbanos, 7 females for korbanos, and a male and a female for species preservation. (And same for the birds!) According to others, 14 of each, 7 of each gender for both korbanos and species preservation.
In addition to the number that Noah was commanded to preserve (7, 14, or 16 mentioned in the preexisting answers here), Haamek Davar notes that Noah was allowed to, and did, bring his personal animals on to the boat. Indeed, he says, the raven and (kosher) dove that Noah sent from the boat were his personal birds. He doesn't indicate how many personal animals Noah had on the boat.
I don't have Haamek Davar before me at the moment to cite it exactly, but it's in his commentary to the verses where Noah sends the birds out and the verse "כי אתך ראיתי צדיק לפני בדור הזה".