We're totally about to drop some knowledge on you: even though some folks might think animation is a film genre, it isn't. Animation is actually a medium or a technique, not a genre.
Think of it this way. You can either paint on canvas or take a photograph, but both could still hang up in an art museum. You can tell a story on film using hand-drawn cartoon characters or real, live actors. Both could be awesome. It's the kind of story they tell that defines their genre.
So which film genres does Aladdin fit into? Well, for starters, it's a comedy. Your first hint should be that they tapped Robin Williams to play to the Genie and shoot out jokes left and right like a wacky gag-dispenser. But aside from packing in the laughs, Aladdin follows the pattern of a typical comedy. Things may go wrong in zany or unpredictable ways, but in the end, the good guys win, the boy gets the girl, and everyone lives happily ever after. Huzzah.
Since Aladdin features five full-length songs written by a Broadway team, you could say it fits pretty neatly into the category of movie musical, too. After all, the characters keep bursting into song at highly emotional moments, which isn't something you see in say, The Godfather.
And, of course, we're talking Disney, and we're talking cartoons, so Aladdin is obviously a family film. That just means the story has something for kids of all ages. The Genie's Peter Lorre impression is probably gonna fly over the heads of the younger crowd, but we're guessing the little ones are gonna enjoy it whenever Iago smashes into anything.