I think there are a lot of dependencies:
1) What do you play against 1.e4? French players, who master the blocked center, would do better with the Kings Indian. Sicilian players, who tend to prefer a more dynamic center, would do better with most lines of the Nimzo. Alekhine players, who like to fight the mobile central pawn mass, would do best going with the Grunfeld. Caro-Kann players, who surrender the center early with dxe4 and holding a compact position would do best playing the Slav. Your 1...e5 players tend to do best with declining the Queen's Gambit with 2...e6. You have to look at your stylistic preferences, like Blocked vs Mobile vs Static vs Open vs Dynamic center.
2. Are you talking over the board and internet blitz, or correspondence, like ICCF, where computers are allowed. Correspondence chess most will play the Nimzo-Indian because it tends to be the strongest with computer assistance, but with the human factor, there is a LOT to know, even more than the KID or Grunfeld.
Hope this helps.
I have been trying to improve my chess game as black against 1.d4, and I am not sure which opening to learn. I have been looking various options like the Grunfeld Defence, The modern defence, The Slav defence, the Nimzo-Indian defence, the Dutch defence and the King's Indian Defence, but I have yet to settle on one.
I am interested in hearing your opinions on the matter. Which opening do you think is the most effective against 1.d4 as black, and why? Have you had success with a particular opening in your own games?