It's difficult to find a more agressive opening against 1.d4 than the King's Indian Defense (KID). As most of the hyper-modern openings, it voluntarily gives up the center in order to attack it later. But unlike many other openings with a similar concept (like the Grunfeld Defense for example), in most of the cases the real target of the opening is White's King. It shouldn't come as a big surprise if you know that credit for the development of this opening goes to three Grandmasters famous for their fierce attacks: David Bronstein, Isaac Boleslavsky and Efim Geller. The King's Indian Defense was always very popular amongst all kinds of chess players from beginners to World Champions. Three of them (Mikhail Tal, Bobby Fischer and Garry Kasparov) used the KID as their main weapon against 1.d4 for the significant part of their chess career.
This is one of those openings where you really need to understand the spirit of the opening rather than memorize particular moves. The lack of knowledge of the typical ideas can quickly turn a promising attacking position into a passive nightmare. That's why if you want to learn this exciting opening, analyze the games played by the above-mentioned players. It will help you more than countless opening books. Here is a simple example. Say you want to get some ideas about the KID and check an article about it on Wikipedia. Describing the opening, it says: " Play goes 1. d4 Nf6 2. c4 g6 3. Nc3 Bg7 4. e4 d6! ". Impressed by the exclaim after the last Black move 4...d6, you might think that it is the best and only way to play the KID. But let's look at the next game of Fischer (Please remember that like in most of my articles, the games are given as tactical exercises but you can always replay the whole game from the first move if you click "Solution" and then "Move list".)
As it turns out, 4...d6 is not the only move and 4...0-0 is not worse at all. The point here is not to disparage Wikipedia or the nameless author of that article who did a decent job. It just shows that when we talk about chess in general or the KID in particular, there are not many sources that understand the subject better than Fischer, Tal or Kasparov. And talking about Tal, the game I want to show you is typical for him. Your computer will probably tell you that the attack was unsound, but as Tal himself said more than once: "Analysis after the game and a real game are two completely different things." I cannot agree more and doubt that many chess players would be able to withstand his vicious attack in the next game.
Garry Kasparov played the KID starting from his first tournaments in his Pioneer's Palace till the World Chamionship matches. He created many masterpieces there, like the next one:
The last game I want to present wasn't played by World Champions (just by two strong GMs). But it demonstrates very well why the KID wins many hearts among chess players.
If you like to attack and never played the KID (is it even possible?), do yourself a favor and try it. You'll be in a good company!