Do: Kill off a main character
The Bourne Supremacy begins with a gutsy twist: The surprise assassination of Franka Potente’s Marie, who gave the first film much of its emotional resonance. The gamble paid off: Supremacy and Ultimatum are both supercharged by the title character’s quest for vengeance.
See Also: Scream II, The Dark Knight, and The Godfather Part 2. Harrison Ford always felt that Han Solo should’ve died in Return of the Jedi, which in all fairness would have been totally awesome.
The Bourne movies are one of the few trilogies that gets better as it goes on.
Screencaps from both movies are up in the gallery.