This only goes for one ability used in one turn. I won't bother listing the Quick+Ultima/Quadra Magic/Mimic/W-Summon kind of stuff. Also, this only lists potential damage; for example, I personally have never seen powered Cid up to the point where Highwind would actually deal 9999 a hit.

Final Fantasy V
Sword Dance: 19,998 (9999x2)

Final Fantasy VII
Knights of the Round: 129,987 (9999x13)
Shotgun Ultimate War God Champion Slash (a.k.a. Omnislash): 149,985 (9999x15)
All Living Humans Must Perish (a.k.a. Doom of the Living): 149,985 (9999x15)
Anger Max (a.k.a. Ungarmax): 199,980 (9999x20)
Highwind: 199,980 (9999x20)

Final Fantasy VIII
Lionheart: 159,984 (9999x16)

Final Fantasy X
Attack Reels: 1,199,988 (99,999x12)
Magus Sisters - Rag (a.k.a. Mindy) - Returnal (a.k.a. Passado): 1,699,983 (99,999x17)

Final Fantasy X International
Magus Sisters - Delta Attack: 599,994 (99,999x6)
Anima - Chaotic D (a.k.a. Oblivion): 1,599,9984 (99,999x16)

Final Fantasy X-2
Quick Trigger (a.k.a. Trigger Happy): 199,980 (9999x20)
Quote Originally Posted by Necronopticous
1199988 is easily attainable in Final Fantasy X with Wakka's Attack Reels, in the history of Final Fantasy games it remains the largest number of damage that can be dealt in a single turn.