I was a major fanatic of the Matrix when it first came out. To illustrate how much, I watched the first movie once a week for probably 6 months, during 1999-2000. So it's very safe to say that I've seen it. I also lost my virginity to my ex-girlfriend with the music from Zion playing in the background. ;)
I just read koreandrunkhobo's review, though. I realised that in hindsight, I couldn't disagree with anything he said. Yes, it redefined the word, "pretentious." Yes, it was mainly intended to look cool, and there were plot holes all over the place, and yes, other than lip-locking with Trinity, as a character Neo doesn't really develop very much.
The best movie of the trilogy is the first one. I haven't ever seen anyone disagree with that, even among people who liked all three. There are some who've said that the latter two movies, strictly speaking, are not even real sequels at all, but are based on The Animatrix, which was their source material. Again, I agree. If you watch the first movie, and then the Animatrix, you will notice differences. It's subtle, but they're there.
Although not as good as the first one, Reloaded was still solid, although it is a balls-to-the-wall action movie, whereas the first movie only really got busy in the last act, and is mainly dialogue before that. Revolutions was fairly lame, and wasn't remotely close to what I was expecting; although it does have some good moments.
The other thing that sucked about the sequels, (particularly Reloaded) is that they feel like a Valentine from the Wachowskis to George Lucas. The Kid could be considered The Matrix Trilogy's answer to Jar Jar Binks. Commander Lock was also incredibly annoying; how did the Council ever put that idiot in charge of Zion's defense?!
The Animatrix was something of a mixed bag. You do need to see it in order to completely understand the two sequels, but some of the shorts are better than others. From memory "Matriculated," was my favourite, although "The Second Renaissance," has most of the exposition.
The series as a whole is worth seeing, if only to know what all the fuss was once about. Truthfully, I still consider the first film (and only the first film) to be one of the most important things that Hollywood has ever done; but don't expect as much perfection as some have claimed. You won't find it.