http://www.youtube.com/watch?v=AmZEI_JIm3k&ob=av3n
Bioshock's was rather good, especially when you consider the subtlety of what was written on the card of the present.
In response to the OP in particular, the first Darkness had a superior opening. It actually set the atmosphere, only mentioning anything supernatural in the cryptic sentence "That was the first time I died" which let the player know that there was certainly more to come while not breaking the immersion in the visceral world that they are placed in, unlike The Darkness 2 which shows no restraint, subtlety, or regard for atmosphere. There were times in the darkness 2's opening that I actually laughed a little.
I think that's what makes a good opening, subtlety and accurately setting the scene in a suitable manner that lets the player feel immersed due to it being at least partially interactive, and having a slow(er) build up rather than being thrown into a fight scene (The Darkness, the Half Life games, Bioshock, System Shock 2, Escape from Butcher Bay).
A bad opening is akin to that of the darkness 2, making the player sit through a non-interactive cutscene while a single character (although a well acted one in this case) spouts over the top action movie lines in a pretence of badassery, saying "THIS IS COOL ENJOY IT NOW" rather than letting the player get an appreciation for the game.
I suppose that rant I just accidentally produced applies more to opening sequences as a whole rather than just opening 'cutscenes', but I've seen Bioshock noted so I assume sequences are fair game here (?).