The most aggressive may not be the most sound and vice versa, but my vote goes to the nimzo-indian. I play mostly slavs and kid myself though..... go figure
What is the Most Aggressive (and Sound) Defense to 1. d4?

I have a game from Kramnik Vs Anand
1.Nf3 Nf6 2. c4 e6 3. Nc3 d5 4. d4 c6 5. Bg5 h6 6. Bh4 dxc4 7. e4 g5
8.Bg3 b5
Black is up a pawn and has played rather aggresively although his position is weakened, with correct play, black can hold on.

Is it possible to be aggressive and sound? :)
Don't Know for sure but i would point out that aggression leads to double-edged positions that could go either way based on the play. when you play aggressive you take chances personally i would say that you can play sound and aggressive but you have to be accurate in your moves

How about the Chigrogin defence, or the Albin counter gambit ?
I play the Chigorin currently as my main defense to d4. I think it is aggressive and gives very good chances as long as you know your stuff. You will also get very different types of positions. You have to be willing to go for a positional struggle as well as a tactical slugfest, you have to be comfortable playing with 2 knights against 2 bishops and the other way around.
Is it sound? I'm not so sure. I think there are a couple of lines that need patching up, like the mainline:
Or for example this line I played in a game on here:

How about the Chigrogin defence, or the Albin counter gambit ?
I like the Albin too. Been playing it just a bit this last year and it makes some amazingly "wealthy" positions, rich with play and ideas. It seems to me to be one of those openings one could spend a lifetime studying for interesting new ideas, and be entertained the entire time.
And it makes many positions where WT can find himself in trouble if he drops only a single tempo. (Which might be a pretty good determinant of how "aggressive" an opening is. EG the Dragon for another, and Polugaevsky Najdorf, seem about the most aggressive openings in existance by that standard.) Even WC Euwe, though he won, had far from an easy game against the Albin. If one is interested in the Albin, they may wish to see IM J. Silman's website. I liked his article on it very much.
As is being said, Nimzo-Indian is certainly a good opening, if you like those kind of positions. Personally, I Don't. Not the positions of the traditional NI. Though in Postal play, I did specialize in playing the black side of the ...b6 Nimzovich, as recommended by Fischer in his "60 Memorable Games" book. It produced 2 winning games (of 2 attempts) for me in Master level play and one was quite an interesting tactical game, won combinatively. The other was just to grab a pawn and hold on to the better position.
My own mainstay was the King's Indian. You are either a "believer", or not, when it comes to the KI. But in over 10 years of Postal, there was only one variation it ever lost to. You MUST be prepared to make active and passive sacrifices, as called for however, to be able to play the KI. Not just to play it effectively. Rather there are often games where you Must Win ... or LOSE. To sac or not is usually not optional when the opportunity occurs.
I used the Grunfeld as a secondary opening. It is still very strong and not only wealthy with, but also ripe for producing new ideas at this time. But it takes a lot of study to be a proficient Grunfeld player, as there are so many variations & lines ...and it is usually White who gets to determine which of them you must enter into. But if you did trouble to learn this opening, I think you could use it always, no matter what level of play you attain. imo. It was also a secondary opening of Fischer and Kasparov, and played by Smyslov among others.
KID and Benoni are my favorite.
I think that 1... d5 tends to give white a good positional advantage...

I wouldn't try to argue with a NM Ozzie cobblepot
Haha you totally should because that's what this website is here for!

This is my favorite part of chess. The fervor with which people attempt to convert others to their favorite openings. It beats politics or religion any day for an argument.
FWIW, I play the Dutch Stonewall.

Benko Gambit.
1.d4 Nf6 2.c4 c5 3.d5 b5
What do you play (that is both aggressive and sound) against 1.d4 Nf6 2.c4 c5 3.Nf3
3...cxd4 4.Nxd4 e5 5.Nb5 d5!?
GMs still play it, so I would guess it is still sound.
I think this is a better line for black (A31 ~ The Kasparov Gambit) than is the Benko proper.
Seriously? That has not been my experience with either opening.
But why?
well i feel best defence is the you are comfortable with