I've played through Final Fantasy VIII so many times, all the scenes are a little kind of repetitive and boring. But I'll try to dig back to the first moment I picked up that PS controller and placed that shiny disc into the disc reader.

In chronological order, (Warning, Minor Spoilers)

Best Scenes

Dollet Field Exam - Dude, that scene where Squall looks up from the boat just takes the freakin' cake.

Exploring Timber for the first time - It was nice. A real actual town to explore in.

Galbadian Garden - Nice plotline development. And Irvine's an idiot.

Deling City Assassination - One of the best parts in the game. Except the sewer part.

Missile Base - Some of the stuff they say is just way too funny, depending on the party members you choose to infiltrate with.

Balamb Garden at FH - Choosing a band and that whole Squall + Rinoa scene was way too cool.

Balamb Garden VS Galbadia Garden - Another top notch scene I'd play again any day.

Lunar Base - Nice plot development. And seeing Riona like that made my heart bleed.

Ragnarok - Music was awesome, Propagators are scary, and tough. But it's a test of your strength, and the reward is amazing.

Lunatic Pandora - I loved the opening scene where Ragnarok totally pwnz the shields.

Fighting Jumbo Cactuar - Leviathan ftw. And Cactuar = 20AP ea. ftw.

Fighting Bahamut and Ultima Weapon - Pure awesome intense fighting. The questions were a little gay, though, and the whole stairs down to the bottom to Ultima Weapon were just killer.

P.S What is with everyone grinding up to level 60? Don't you know that enemies level with you? Your actually putting yourself at a disadvantage if your high level. I beat the game at like, level 30. It's just good magic to junction with, and AP for great GF skills, that's all you need to do good in the game.