Seymour Summons Anima - This is a moment that doesn't stick in my much after I've played FFX, but I'm always a little caught off guard by it when it happens. Up till this point, the party's been doing the anti-fiend fighting, and has been competent at it. They save the SS Liki from Sin, defeat Ochu and Sinspawn Geneaux on Kilika, and then save Yuna from the Al Bhed (not strictly fiends, but whatever), and are even holding their own against the monsters in the Blitzball Arena, bolstered by Auron. But then Seymour summons a depraved looking Aeon which annihilates the fiends with singular blasts, in a beautiful FMV, and leaves everyone, the party included, stunned. The upshot is that Seymour's an immensely powerful summoner who's just saved many lives. But it is later revealed (by, IIRC, a Guado outside Bevelle) that Seymour released the fiends himself, in a scheme to win the admiration of the people. From hero to schemer. Probably a better moment than it gets credit for, largely because it comes before and after more talked about ones (the Luca match, the Auron/Tidus heart-to-heart and the laughing scene).
Via Purifico - After the pulsating action of the attack on Bevelle and the drama of the trial, Via Purifico appears to serve as a kind of reflective period for Yuna. It's the only part of the game where Tidus isn't the field character (I like to imagine that in Zanarkand, at the campfire, Yuna feels compelled to take over the narration, and that's why we see her on the field). But in fact, thanks to the dangerous situation Yuna's thrust into, and the relentless (and beautiful) piano piece in the background, it only amps up the tension. At first, simply surviving is difficult, then you need to find your way through an awkward maze. It's one of the most "non-linear" areas in the game, in so far as it requires exploration to collect all the chests and find each character (one can, of course, in what I perceive as irony, escape the Via Purifico by walking in a straight line). Auron is upset enough about being there that he remarks "I hate this place" - pretty unusual for him to show frustration like that. It culminates in a summoner battle (the only mandatory summoner battle in the game which you can be Game Over'd in) between Yuna and Isarru, who's been sent to finish off the 'traitor'. It's a fitting end to Yuna's escape that she shows her superior skill and defeats him, becoming the only summoner we've seen to be still journeying.
There's also the Evrae Altana bit of the Via Purifico, but who cares about that.
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We are living our lives
Abound with so much information