The first offical video game based on The Matrix license was developed by Shiny, published by Atari (formerly Infogrames), and was released on May 15, 2003 (for all three consoles and the PC), the same day as the second movie in the series, The Matrix Reloaded.
The movies got more than a little of their inspiration from video games, so it's only fitting that the brothers Wachowski would want to make a video game in turn based on their movies. The hype behind this game was phenomenal: first the fact that this is the fucking Matrix we're talking about here (the most major action movie in many a year), and second the fact that apparently the sibling directoral pair was helping personally with development of the game, and not just shilling it out to the highest bidder.
Of course, like I said, this was all just hype. Exactly how true it is, or whether it matters, remains to be seen. What does matter is this: is the game any good? Is it the completely new, wonderful thing that was promised, a new tie to bind movies and video games together, an unprecendented leap forward in entertainment?
Well, no. It's a video game. We've played these before, remember; bits of action interlaced with cutscenes. They're good cutscenes, granted: they filmed them right alongside the movies, with the same actors and sets and special effects. They don't suck, unlike many other games' cutscenes I could mention. The game itself? It's fun, sure. You could easily blow hours playing it, but it's not entirely groundbreaking. Remember Oni? That was a game where you ran around either beating people up, or taking their guns and shooting them. And remember Max Payne? That game had a bullet-time mode as one of its primary gameplay gimmicks, a mode lifted straight from the first Matrix movie (so it's not suprising they'd want to use it in the actual Matrix videogame; this gets you into a tangled mess of whether this game stole the feature from Max Payne; either way, we've seen it before). This plays like a combination of the two, more than anything else, with the occasional rail shooter or racing game thrown in for good measure.
Of course, the beating-up of people is better done than in Oni: they've got people who actually know about various forms of martial arts designing the fighting system. And the bullet-time is better done than in Max Payne: turning it on allows you to access all your most powerful and fantastic moves, like running and jumping off the walls and dodging bullets. So saying this game is a combination of two older games isn't at all degrading it because it does each respective game better than the original.
It's important to note that this game seems to do better on the console (there is already a patch available for the PC version, two days after release; whether this means there's something wrong with only the PC version or with all four versions, I do not know; remember that there was a very strict release date associated with this game, which is never a good thing, and combined with a quadruple platform release...). I have only so far played the Playstation 2 version. The PS2, being the oldest of the current generation of consoles, offered a game which seemed like a little detail had been removed, but still looked quite good. The one quirk I noticed, which was truly annoying, was that some of the in-game cutscenes had a strange "echo" effect when people talked. This only happened in some of the cutscenes some of the time, but made it very hard to understand what people were saying when it did occour. I can only guess whether this oddity found its way into the three other versions. The controls were simple once you got used to them: three separate buttons for fire, punch, and kick is basically how it breaks down, with others for jump, "focus" (bullet-time), and so forth. In many games where you can both shoot at bad buys and beat them up with fists, you must manually switch between these two modes somehow. In this game, you just hit the button and things happen. Shooting is easy: face in the general direction of a bad guy and hit the button; you'll hit them. Fighting is easy, seeming more like a stripped down two-button fighter than anything else.
The game is a decent action game, with martial-arts stylings. It starts out fairly easy, but gets reasonably difficult later on. I'd recommend picking it up, but don't expect the most revolutionary (or even well-polished) game. Maybe wait for a price drop if you're iffy about dropping the $50. Fun but not earth-shattering.