Is it The Arrival? Main star of that is lead in a show right now, and it fits the timeline per https://secure.wikimedia.org/wikipedia/en/wiki/1996_in_film#April.E2.80.93June
You got it. I never saw that one.
Yes. 
I can’t believe how hard that one was.
I wouldn’t have gotten it without the release month/year. Thanks, Wikipedia! 
(that still counts as research, right?)
He is afraid. He is totally alone. He is 3 million light years from home.
Howard the Duck? d:
Cloverfield? (not likely)
ET: The Extra-Terrestrial?
bangs head on desk
Heh. 
A world where the mighty, the mad, and the magical will have their final battle.
Conan?
Baltar
Red Sonja while I’m at it?
Dune?
No and no.
Dune?
Damn it. 
Your turn.
Good thing. I was out of ideas.
I’m not sure how popular this one was. Good luck.
What if you discovered the most dangerous man in the universe was you.
The One, with Jet Li?
Good. How’d you guess?
Your turn.
I actually watched it for the first time maybe three weeks ago.
Pretty good movie, IMO. Definitely a victim of bad timing, considering it really wasn’t anything like The Matrix.
Your turn.
On October 10th, speak softly and carry a big sword.
Is that Kill Bill?
Final Fantasy: Advent Children? Biggest sword I ever saw…
Oh! Oh! Sean Connery movie, on Alcatraz…THE ROCK!
I see that I am behind. Is this one the Three Musketeers remake?
You are correct sir! I stepped out and did a bunch of errands, sorry about the delay.