To be honest.. The concept of the Matrix is not original. I got rejected by Asimov's in 1989 with a short story of *very* similar material -- man wakes up to find he's been living a monitored dream life. I believe that the wachowski's had a better spin on the concept than my own.
I've traced the idea back to Aeneas' trip to Elysium in the Aenied. Aeneas leaves through the gate dreams go through, implying that the rest of the story is all a fantasy. This makes the foundation of Rome a dream, and consequently all history. I think it goes further back than that as well, Georgias and the Sophists. Then there's the Amazonian Amerindians beliefs that the world is a fiction underlying the reality of dreams.
More recently, it rips a HUGE amount of visuals, setting, atmosphere and philosophy from the Japanese film Ghost In The Shell. Ghost In The Shell also gets way too into the philosophy so the last thirty minutes or so are almost incomprehensible.
That said, it's a fun film. I don't think it's the philosophical masterpiece that many say it is, but the fights are pretty awesome (look at how many films have leather and kung fu, that's mostly the legacy of the Matrix, although Blade did it first), the specials effects aren't bad and it's good to watch Hugo Weaving just glorying in being a total bastard.
Why is it generally regarded as a great story?
It's not a bad story, as Jcomp says, it's a giant missed opportunity. The fact that the majority of humanity would be destroyed by shutting down the matrix is referenced once, and then thrown away for the rest of the movie. Although the speed to which the main characters gun down elderly security guards is pretty indicative of their basic world view (The "liberation" "Humanity" is more important than individuals). There could have been some fantastic speculation here about people, rather than the hogy Christian/Bhuddist/elementary philosophy symbolism crammed down our throats.
I have never seen the third film, but after I saw the first one I made up the ending, and I really think they should have gone with it. Neo kills Agent Smith or whoever big bad is and shuts down the matrix. Everything goes black. Cut to him on one of the seats they used to hack into the matrix. His heart monitor flatlines. Machines cluster around him, it was all an experiment into human nature and how to control them easier. Or alternativley, have Neo fighting his way through a neverending series of matrixes forever.
What are some things you notice/recall about the Matrix?
I remember Hugo Weaving being an extraordinarily menacing antagonist, and Keanu being wooden and boring (he also only said "whoa" once and didn't even say "bogus"). Lawrence Fishburne was pretty cool, but I got a whiff of the Magical Negro at the start, that faded out though thank god.
How did the unconventional structure enhance the story?
It didn't have an unconventional structure. It went from the beginning to the end in chronological sequence without any flashbacks or forwards. The first act was the first act, the second the second, and the third the third. Don't mistake flitting between multiple computer programs as unconventional structure. It probably wouldn't have worked with anything experimental, it would be too hard to follow.
Discuss the Matrix's use of story elements: characterization, foreshadowing, rising action, etc.
The characters, apart from Smith and the Agents (who are pretty good machine characters, almost uniform, no discernable characteristics). The human characters are standard action movie archetypes. We have average joe who is the only one that can save the universe, wise mentor who is in peril, Judas, the GURL, and a slew of other characters who appear to have no purpose other than to stand around and look cyberpunk.
I didn't realise very much foreshadowing really. I can think of plot points, like the Oracle being all 'You are not the One', perhaps 'in a next life' is foreshadowing to the end. The rest I'm not too sure on, but it's been a while since I saw it.
