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 Magitek 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.
Rourke's laconic reaction to Leviathan.
Rourke: Tell Cookie to melt the butter and bring out the bibs, I want this lobster served up on a silver platter!
Milo, who for the first half of the film wasn't allowed to touch anything for fear of screwing it up, showing everyone how to operate the flying machines.
The Guardians of Atlantis being activated and shielding the city once more, this time from the exploding volcano.
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.