What if I told you Morpheus never actually says "What if I told you..."? The origin of this meme stems from a simple jab at the film's twist, which featured a photo of Morpheus simply asking "What if I told you... The Matrix is all inside a computer?" Since then, people have just taken it from there.
One of Agent Smith's more famous quotes is often written as "But Mr. Anderson, how can you make a phone call when you cannot speak?" or something similar. The actual line is "Tell me, Mr. Anderson, what good is a phone call if you are unable to speak?"
Development Gag: A deleted subplot from The Matrix reveals that Morpheus has previously believed five other people to be The One, all who died after attempting to fight the Agents. In The Matrix Reloaded, the Architect explains that there have been five previous versions of the Matrix before the current one, each with its own version of the One, meaning that Neo again has five predecessors.
Dyeing for Your Art/Important Haircut: "Spoonboy's" mum was very reluctant to have his beautiful locks shaved off. Also, Neo's in-Matrix scenes were shot first, and his on-ship scenes shot last, because Keanu got his head shaved during filming.
Edited for Syndication: Basic cable cuts of the film frequently substitute "Shucks" or "Smokes" for "Shit", and change Neo's line in the interrogation room scene to "How about I give you a flipper?", while completely cutting the actual middle finger (and, by consequence, the "You give me my phone call" part of the line). Also "Jeepers creepers (originally "Jesus Christ"), that thing's real?!!!"
The AMC edit, in particular, changes one line to "I'll bring that whole cockamamy (originally "goddamn") building down".
Executive Meddling: Dropping the original idea of Human Resources being a vast neural net for the more literal concept of human Duracell batteries because Viewers Are Morons. Giving all the other stuff that has to be explained (or not) in this trilogy, one wonders why this idea was so difficult to put across.
Originally, Will Smith was offered the role of Neo, but turned it down for his part in Wild Wild West. To his eternal woe.
The "mental projection" of the Matrix would have been plot-relevant, with Switch (the butch blonde woman and only other woman in the crew besides Trinity) appearing as a woman in the Matrix, but a man in the real world. This is perhaps mirrored by Larry AKA Lana Wachowski coming out as a transgender woman in 2012.
The Wachowskis were given the choice of making the Matrix sequels or Batman Begins. Imagine that...
Jet Li and Michelle Yeoh were initially offered the role of Seraph; Li, who the role was written for, asked for an equal salary to Reeves' and didn't get it, while Yeoh had scheduling conflicts.