ITT we discuss the best anime intros we know. When in doubt about if you should focus on music/animation, choose music. Otherwise, the two can't really be separated so try to assess the whole things.

Try to keep to one intro/post for increased clarity and activity. No age requirement for the intros, but don't just discuss the two last seasons.

The obvious threadstarter is of course:
the Neon Genesis Evangelion intro.