The King's Indian Defense (ECO E60-E99) is an excellent choice for Black, a very powerful and practical. 1.d4 Nf6 2.c4 g6 followed by ... Bg7 and ... d6.
Attack against 1.d4

Albin Countergambit - 1. d4 d5 2. c4 e5 3. dxe5 d4 4. Nf3 Nc6 5. g3 is the start of the main line.
Budapest Gambit - 1. d4 Nf6 2. c4 e5 3. dxe5 Ng4 and here 4. Bf4/Nf3/e4!? are all mainlines.
If white plays some offbeat stuff on move 2 (2. g3 for example), obviously you're on your own.

Hello all,
What is an attacking line for black against 1.d4? It should be stable cause I'm a real attacking player.
You have already mixed two things which do not come together.

Attack is not wise unless you are in a position that is very rewarding for doing so.
You should be defending in my opinion as Black until White opens up and leaves himself vulnerable.
White advantage: Tempo.
Black advantage: Natural defense/Waiting-For-White-To-Blunder.

Dutch is definately a good choice. If you want to play more or less agressively you can pick which variation you want to play. I wouldn't recommend the KID or Benoni simply because they don't give you the confidence you get with other defenses due to how convoluted their positions can get.
Budapest gambit.
Here is Howard Stern ripping white open with the budapest gambit.
There are many lines in red make sure you see them all.
Budapest is a very sharp attacking line where white doesn't have to make too many mistakes to see his position get crushed.

Hello all,
What is an attacking line for black against 1.d4? It should be stable cause I'm a real attacking player.
You have already mixed two things which do not come together.
Oh well I'm sorry, Let's leave out stable and only attacking is there. I want an attacking opening.
Thank's all for your response. I welcome more suggestions.

Sort- of. The Budapest can be dangerous only if white clinges to his pawn. But in most mainlines, it is Black the one who risks falling in passivity.
The analysis you have posted is highly irrelevant, starting as early as move three- no white player who isn't a total patzer will play 3.d5.

Can you explain why pfren? It seems maybe timid, or being unaware of theory.. but isn't "total patzer" a bit harsh?

Budapest gambit.
Here is Howard Stern ripping white open with the budapest gambit.
There are many lines in red make sure you see them all.
Budapest is a very sharp attacking line where white doesn't have to make too many mistakes to see his position get crushed.
Suppose white takes the pawn?

Can you explain why pfren? It seems maybe timid, or being unaware of theory.. but isn't "total patzer" a bit harsh?
White does not accept the offer, lets Black develop another piece at a good and safe post, and does not develop any of his pieces. Ain't that enough? General opening principles should suffice to persuade you that 3.d5 is a bad move.
@ Sutirtha11: Read post #7. It's not the whole truth, but close to that. There is no way to attack, unless white has committed himself to "something".

Thanks for your help IM pfren. But what would you suggest as the natural defence for black against 1.d4?

Any sound defence is "natural"- just don't mess with a lot of opening theory. That is the KID, the Grunfeld, the Modern Benoni.
What about something like the QGD Tarrasch, or QGD Chigorin? The latter seems good enough for Morozevich and a few other GM's, so it cannot be that bad for you- and the theory you have to learn is just a small fraction of the one in most mainstream openings.

Thanks a lot IM pfren. Of course it will be good for me. Can you recommend any book/website for the opening that you recommend? I will be just starting out with it.

What about this one?
http://www.newinchess.com/The_Chigorin_Defence_According_to_Morozevich-p-382.html
Written by Barsky, but Moro has made many vital contributions to it. IMO it is an excellent book, full of very instructive games.
Hello all,
What is an attacking line for black against 1.d4? It should be stable cause I'm a real attacking player. Put simply - I like to attack. Somehow or the other I always got into trouble with the KID. I don't mind studying little or so opening theory.
Thanks in advance!!!