FFVI would be my number one, with that storybook ending that gives one final scene devoted to each of the characters as they escape Kefka's Tower, their individual strengths coming into handy to help them survive along the way. The Locke and Celes moment completes both their character arcs beautifully, and is a tearjerker. Then after going through presenting every character the storybook ends with "and YOU", gets me every time. Then the game has one final source of tension in Terra's fate, and they made the right choice in the end by having her survive.
FFX is a very close second...I start bawling after Yuna falls when she goes to hug Tidus. Auron's goodbye is awesome, like everything Auron does is. That final high-five between Tidus and Jecht is the cherry on top, Tidus's character arc complete. I think this would be my #1 if it ended at the high-five, even though I like Yuna's speech it's emotionally unsatisfying compared to what came before, and should have been saved for the beginning of X-2.
FFIX is third, very different in execution to the point it's more an epilogue than an ending, but perfectly bittersweet between learning of Vivi's fate but also getting Zidane and Garnet reuniting.