Code Geass and Neon Genesis Evangelion have poor intros for the series in their choice of songs, the styles do not really fit the anime's as far as I am concerned. They are kind of cheesy, and a bit too upbeat for the type of show.
The best intros on the other hand (in no particular order):
Death Note
Ghost in the Shell Standalone Complex (both seasons)
Darker Than Black (first season)
Elfen Lied
The best intros on the other hand (in no particular order):
Death Note
Ghost in the Shell Standalone Complex (both seasons)
Darker Than Black (first season)
Elfen Lied