The ascension of Kida in the Crystal Chamber is probably the most memorable part of the movie, and generally the reason it's still recommended today. Any part with Kida as the Crystal is extremely impressive in animation, music, and mood.
The entire opening, although watching Kida be forcibly separated from her mother due to the Heart may also count as a Tear Jerker.
The Leviathan attack scene is terrifyingly awesome. A Magi Tech monster big enough to be measured in miles, a desperate battle for survival with torpedo-toting subpods and turrets, and finally a hair-raising, skin-of-the-teeth escape through a twisting underwater chasm.
Of course, there's also Rourke's rather laconic reaction to seeing the Leviathan.
Rourke: Tell Cookie to melt the butter and bring out the bibs, I want this lobster served up on a silver platter!
Heck, everything that Milo does during the climax. Riding an ancient flying machine into battle against Rourke's more ruthless crew to save the crystal-infused Kiva, driving said flying machine into the escaping balloon when all other attempts to stop it fail, and refusing to back down against Rourke himself despite being woefully outmatched. Bonus points for using his wits (and a crystal-charged shard of glass) to ultimately beat his stronger opponent!
The Guardians of Atlantis being activated and shielding the city once more, this time from the exploding volcano.
Creepy Awesome: It's mentioned in the DVD commentary that after test screenings, the filmmakers asked kids what the scariest scene in the movie was. The answers were invariably either the climactic battle or the Leviathan. Kids were also asked what their favorite scene in the movie was... and the answers were invariably either the climactic battle or the Leviathan.