The rules are simple. The game starts with a basic rule: Draw one card, then play one card. Each player starts with three cards. The player with the longest beard goes first. (Darn it, I just shaved.)
The cards include Keepers, cards you play in front of you with simple concepts (Cookies, Milk, Moon, Love); Goals, which state the victory condition (e.g., Milk and Cookies, which means whoever has Milk and Cookies in front of them wins the game); Actions, which allow to do things (e.g., draw a card from the player next to you or mix all the Keepers around), and Rules, which change the basic rules of the game.
It's the Rules cards that makes the name "Fluxx" so appropriate. The game is constantly changing as Rules and Actions change the nature of play. Those who dislike Fluxx usually say that they don't like the fact that it's hard to plan a long-term strategy; you build up a plan, then someone plays a "Draw 1, Play All" Rule and everything goes out the window.
Looney Labs has released several variations on the game, usually by incorporating different Keeper and Goal cards, along with Creepers, which can keep you from winning unless you get rid of them. Among the variants are Martian Fluxx, Monty Python Fluxx, and Zombie Fluxx. (They used to publish a Legalize Marijuana Fluxx, but not anymore. I gave a copy to Vann; I hope he's still got it.) All of them capture the same spirit of ever-changing game play as the original Fluxx.
Fluxx is a game for those who enjoy a short game with a strong element of the unexpected. If I'm with a group of friends and we've got 15 minutes to kill, I'll usually say, "Hey, let's play Fluxx!"