What's the Amelie of anime?
In terms of looks? Then Paprika.
Some 2deep4u pretentious hipster garbage? Penguindrum.
I don't even remember the plot that well but I'm going to say Welcome to the NHK.
Style-over-substance work with 'quirky' humor and depicting a highly idealized reality appealing to foreigners? Cowboy Bebop.
Amélie Poulain might be pretentious, hipsterish (though it always was and has been popular---and thus doesn't really qualify), and garbage, but it's certainly not deep.
Perfect blue or paprika
Shitty movie about an annoying cheerful bimbo?
Sayonara Zetsubou Sensei
Holy shit, anon, grow up.
Something about NEETs.
Detroit Metal City.
I really that Chungking Express doesn't get as popular as Amelie. Otherwise it will probably get a slating by fedoras like it happened to Amelie.