In no particular order:
Odin Destroys Cleyra
Odin is pretty badass no matter his appearance, but something about galloping
straight down at Cleyra is so awesome and unspeakably terrifying.
Seymour Summons Anima
Oh man, this scene. Anima looks NOTHING like the Aeons you've seen thus far, what with an anchor dragging this terrible creature out of Hell, and this is your first glimpse at just how powerful they can be. Not quite on the scale of IX's Eidolons, but still, it wrecks all the fiends in the stadium. But why does it seem to cause it pain, you're made to wonder It's eye bleeds at the end. Also, if you still haven't somehow begun to figure out Seymour's alignment, this is likely to give you some serious doubts. Despite the fact that he's saving the spectators.
Sister Ray Fired, Diamond Weapon Destroyed
Nothing's better than a really big gun of course, but the lengths the scene goes to establish the size of the undertaking are great. First, all eight reactors kick on at full power, and feed
every ounce of power into the cannon. I love how the entire city goes dark to fire it. Then you get the typical anime-style really powerful gun absorbs stuff from the air for whatever reason. But then I love how it shows what a rush job it was to put the cannon on Midgar and how nothing was done to brace the gun or the city. All the windows blow out, the scaffolding is badly damaged. It's quite a contrast to how battle-ready the city of Junon was, and a reflection of how much more desperate Shinra is.
FFVIII Opening Scene
{Posted by Splintered}
The best opening scene in the series, bar none. Helped, no doubt, by that incredibly tense, climactic song. A lot of foreshadowing goes on here, of course nothing you'll get at all until having played the game, but it's fun in retrospect. And it's fun piecing things together, especially as you are introduced to characters featured in the scene. And, of course, it's a sweet fight scene, probably Square's first. Showing the use of magic and gunblades. Also the feather turning into the sword was a nice touch.
Welcome to Gran Pulse
Best FMV in XIII, easy. And it is absolutely gorgeous. The view of Pulse is pretty stunning, both from high up and when they're flowing low to the ground. It's such a drastic change of scenery from Cocoon with a wide open, untamed wilderness (also signalling the point where the game opens up). But it also wastes no time showing why Pulse is something to be feared. That giant ugly Fal'Cie comes for them immediately.
And the way Fang and Lightning summon Bahamut is freakin sweet.
Breaking through South Gate
I've loved this scene ever since I was a kid. It's just so exciting, nothing like a good old fashioned chase scene. And it's made better by the chase of two pretty pedestrian airships by FF standards. Furthermore, any use of magic outside of battle is always welcome to me and you get to see Vivi stick it to Black Waltz, having just watched what happened to the dolls.
The derpy look on Black Waltz's face before it blows up is a little hokey and I could do without it, but that's FF9 for you ("F your consistent tone!")
Sephiroth vs Genesis vs Angeal
Yeah, yeah, you hate Genesis, I know. But this an awesome scene all the same. It does nice story stuff like exhibit the nature of their relationship and everything, but it really does establish Sephiroth and unequivocally their superior. He's clearly having fun and Genesis, with the use of magic can hold is own. And, on that note, it's nice to see A)someone in the Compilation using magic in cutscene and B) not simply casting a spell, but using it and manipulating it. Not only with the fire spell, but powering up his sword (Elemental? merely a limit move?) But then when you see Sephiroth really turn it on, and there's no question, as he slices the cannon into ribbons, effortlessly - indeed, as collateral damage.
We all have preconceived notions about Sephiroth going in, but going in without those, it does a pretty good job portraying that you don't screw with Sephiroth lightly, something a first-time player would surely have in mind when it comes time to fight him in Nibelheim.
. Good visuals? 
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