Big Bad: From a meta perspective, she was created in order to give the film a traditional main villain.
Cruel and Unusual Death: All her organic components were burned off, with her screaming the whole time. Her severed robotic head and neck appeared to still be functional afterwards, so Picard snapped the neck to deactivate her.
Hive Queen: Though she never claims to be the Queen.
I Am the Noun: "I am the Borg", and later, "I am the Collective."
Prim and Proper Bun: It's not actual hair, but the mass of wires on the back of her head are arranged in a circular pattern and she certainly has the personality to match.
Remember the New Guy: Captain Picard remembers her when she's first introduced. Could be justified by the fact he was a Borg for a while, but that doesn't explain why he doesn't mention this vital piece of information about a dangerous enemy onscreen, and Data seemingly knows nothing about her despite the fact that he presumably would have read any report Picard made after the incident. They attempt to Handwave this by implying that Picard had forgotten about her until they're reintroduced in the film.
We Can Rule Together: Tries this on Data. It fails, though he seriously considered her proposal for 0.68 seconds. It's also implied that this was her aim with Picard when he was Locutus.
Surprisingly enough, this is mostly averted. While the Enterprise crew does look up to him, they also remember that he was a flawed human living in mankind's darkest period of history. So, while they do get annoyed with his Refused the Call attitude, they don't see him any differently then they did before.
Bunny-Ears Lawyer: Cochrane is one of the brightest minds of his time. He's also a heavy drinker who thinks first contact is best celebrated with whiskey and dancing.
Cassandra Truth: Enterprise would reveal that he attempted to tell people about what really happened during First Contact, but he was ignored and later recanted his claims.
Heroic B.S.O.D.: Has a minor breakdown after being confronted with time traveling heroes from the future who claim he's destined to lead the human race into a new era of history and enlightenment. It results in him trying to run away. Manages to get over it with the help of Commander Riker.
I Choose to Stay: At the end of "Metamorphosis". Given his negative feelings about being admired in First Contact, Kirk's line that "there's a whole galaxy out there waiting to honor you" is now Hilarious in Hindsight.
Screw Destiny: Tries to do so after Geordi describes how famous he is in the future. ("You told him about the statue?")
Took a Level in Badass: Went from being a misanthropic, alcoholic jerkass barely eking out an existence to one of the foremost leaders of the human race during the reconstruction after World War III and the early space exploration days.
Who Wants to Live Forever?: In "Metamorphosis," he's discovered as a 237-year-old man trapped on a planet where he's become a de-aged immortal. He says that "immortality consists largely of boredom."
Cochrane: This other guy you keep mentioning, this historical figure? I never met him. I can't imagine I ever will. Riker: Someone once said, "Don't try to be a great man; just be a man, and let history make its own judgments." Cochrane: That's rhetorical nonsense. Who said that? Riker:[grinning] You did, ten years from now.