Strategies for Playing Fluxx

"It is a dark and dangerous game that requires a strategy that most people would find too difficult to keep track of." --Anonymous

Jazzfish has some tips for new players:

Know the Cards. Know the Cards. Know the Cards. I cannot stress this enough.

If you've got a winning combo, crank it up to Play as high as possible. Final Card Random is your friend now as well.
If you get Take Another Turn, use it immediately. You may not still have it next round.
Hand Limits are nobody's friend. Don't use them unless your hand is 'really really good.'
When in doubt, play another Keeper.
Accept that sometimes you just can't win. In the last round of the finals, a guy had to choose between leaving The Brain (No TV) and All You Need is Love as the goal, in the first round of play. Tough call. He went with AYNIL, which I think would have been my choice, on the grounds that people will have only one chance to get Love in play; if they play another Keeper instead, they're out of the running for it. There's good arguments for Brain No TV as well, though.

Frances, whose tag line is "I'd rather be a perky sort of evil" has another strategy tip:

Know your opponents.

I introduced some of my (non-gamer) co-workers to Fluxx. Knowing that one of them will always play a hand limit if he gets it - with preference given to the Hand Limit 0 - affects how we play. For example, at one largish game, when I played Everybody Gets One, I handed him the Hand Limit 0. And I gave someone playing after him a really useful card. (They never got to play it.)
And Hand Limits & Keeper Limits are definitely your friends when someone else is close to the 10 Cards in Hand or the 5 Keepers & those goals haven't been played yet.

Bear Barrow suggests:

Pay *very* close attention to what has already gone to the trash.

You might not be able to Pilfer that special card if it's down in the discard pile too far - but knowing that your opponent no longer has it.....

Steve Hoffman suggests:

My personal strategy is to get "card advantage" as soon as possible and keep it as long as possible!

If you play draw five then end your turn by trashing the draw rule, you'll gain an edge.
More cards, more options, more edge.

Jason Darrah has a few card combos and general strategies:

Drop a Hand Limit 1, followed by either Taxation! or Use What You Take. This way, your opponents will discard any useless cards that they may have, and you end up with something (usually) good! Card advantage: you. This can work even better with Inflation in play.
If someone has Love on the table with any other Keepers, and you only have one Keeper on the table, don't be afraid to hold off on playing any more Keepers for the time being. People tend to play All You Need Is Love just to get rid of it if the person who has Love cannot win with it at the time. This sets you up play Exchange Keepers, for the win.
Everybody Gets 1 is a great tool for cycling through the deck to get cards that you need. It becomes even better when Inflation is in play. In a 5 player game, you essentially get to take the next 10 cards from the deck, and take the two best cards (at the time) for yourself! Use this when you're looking for a specific card.
Know when to get rid of Keepers. If someone has The Sun and Cookies on the table, it may be better to not play Chocolate, for example. If that player manages to steal it, they will have two winning Keeper combinations. When in doubt, though, play it (especially if you can get a winning combination out of it yourself!).