Ok, here is my The Matrix story.
I missed the movie when it was playing in theaters because I was pretty young and didn't care about movies back then. (When I finally watched it I went like "oh, that must have been the movie where there was a lot of talk about a character that was bending back impossibly and everyone's like how the hell did they shoot this scene?? Man, I am years late!")
The first time I heard -anything- about it is was when my sister, who normally doesn't watch scifi and wouldn't like action films with too long action sequences, came home from one of her girl friends and told me with eyes glowing "my friend had The Matrix on VHS, we watched it and it was excellent!" And I was like, oh yeah, what's it about? And she couldn't really describe it to me, all I remember is she told me that it's about reality, our reality, but it is a fake reality, and how there's some other reality that it's the real one. I told her I don't understand what she means, if the other reality is the real one then why don't we see it but we see this one instead? And she told me this reality has been manufactured by computers. All this sounded incredibly interesting to me, but as I said I didn't particularly care about movies back then and my sister couldn't explain it very well either, and I liked to pretend I was disinterested in what she was saying to me so I quickly forgot about it.
Years later, and I still don't particularly care about movies but I catch a TV ad/trailer for the movie (meanwhile I have completely forgotten about what my sister had told me about it years earlier) and I am blown away by the incredible visuals. Gun fights! Bullet casings! I check a TV magazine we had at home and it says it's about a group of people fighting the "materialistic world" and I am like what the hell is this even supposed to mean (seriously WTF...)? The description was so vague and mysterious and the visuals in the trailer were so slick I suddenly became incredibly hyped about the movie, I really really really had to see it.
And I do. And from the very first moments I am blown away by the action, violence, effects, cinematography, music and script. When the truth about The Matrix is revealed I KNOW this is the best movie I have ever watched and will probably ever watch. I am a gamer and everything about this movie makes so much sense to me. It's like they made this movie FOR ME. (Turns out the Wachowskis were gamers themselves

)
I particularly enjoy the clever script and all the philosophy that has been put in the movie. My mind is actively engaged like it was never before by a movie and every time there's a break for ads I am making 1000 different thoughts about reality, messiahs, computers and so on.
The movie ends (what an ending!) and I can't stop thinking about it. Neo becomes my favorite hero. I realize I have to start watching movies because they are not necessarily mindless, you can say through them very important, thought provoking or clever things! I realize what "cinematography" is, I always thought all movies looked the same, but this one looks different! The camera is being put to places other movies don't put it!
The Matrix, which since then I have watched probably 100+ times (I wouldn't really know how many times, plus the bulk of those viewings was done up to 10+ years ago when I was a teenager) is the movie that made me care about movies. It's the "Star Wars" of my generation. It remains my favorite movie of all time and its writers/directors my favorite filmmakers.