When it first came out in 1999, I was pretty much still fresh out of college, and being an electrical engineering graduate who fell in love with computing since grade school, it was just so awesome. I didn't care too much for actions, but I was blown away by how the world run by computer was depicted. And at the end, however ridiculous it is, Neo was able to actually see the world in 0's and 1's, and thus was able to also control the world. 

I was first put off by very strange depiction of future dystopia, but the ending just makes up for everything. Literally one of my all-time favorites. 

One of my all-time favorite movie is 12 Monkeys, and after that, I had to check out Terry Gilliam's other works. And this also blew my mind, and I found my favorite genre - circular timeline (whether the whole movie is in time loop like 12 Monkeys or like Brazil or Donnie Darko, where short duration is expanded and fill the whole movie and we come back to what the next split second brings).