When White plays 1.d4, it limits Black's good responses in comparison to 1.e4. That's not to say that Black doesn't have plenty of reasonable options, though. And while two moves are by far the most popular responses for Black, there are at least six that deserve serious attention by any competitive player.
While there are 20 possible moves Black could play in the position after 1.d4, these six are seen in close to 99% of serious games.
Here are the top six answers to 1.d4!
The hypermodern choice, Nf6 creates a dynamic imbalance right off the bat by attacking the center with a knight rather than occupying it with a pawn. This usually signals one of the Indian defenses, such as the Queen's Indian or the Nimzo-Indian, and can also lead to the Grunfeld Defence or the Benoni. However, transpositions back into other openings are still possible at this early point. This has become, by far, the most popular response to 1.d4, representing more than half of the high-level games played in most databases.
The other popular response to 1.d4 is to keep a symmetrical position by playing d5. This is a more traditional response, occupying the center and helping to develop the queenside bishop at the same time. Note that both of these moves at least temporarily prevent White from safely playing 2.e4, which would immediately give White a nice strong pawn center.
That's a big reason why these two moves have been – and will likely remain – Black's primary weapons against the d4 opening. Common openings deriving from this line are the Queen's Gambit (Accepted or Declined), the Slav, and the Semi-Slav.
This seemingly passive move is actually something of a placeholder, waiting to see what White will do before committing to a plan themselves.
That means that this move can often lead to many of the openings mentioned above should White play 2.c4, as Black can still play either d5 or Nf6 on the second move. However, it also leaves open the possibility of White playing 2.e4, transposing into the French Defense – an opening normally seen after 1.e4!
The final three moves on this list could easily be placed in any order, as they are played with similar frequency; I've placed d6 here because it shares some similarities with the previous move. Like e6, this is another move that plans to transpose into another opening depending on what White chooses to play. Again, 2.c4 can lead to known queen pawn openings like the King's Indian Defense or the Old Indian Defense. But White can once again play 2.e4 as well, which would lead to either the Pirc or the Modern Defense.
Remember when I mentioned that the two top moves on this list were popular because they control the e4 square? The Dutch Defense, signaled by f5, does that as well. However, it offers a completely different kind of position than the more popular d5 and Nf6 options, usually leading to a positional battle. These can be dangerous waters for those who aren't familiar with the Dutch, and draws are less common after f5 than in most 1.d4 lines.
Our final option of note, g6 is yet another move that tends to transpose into other openings and thus isn't really considered indicative of any one opening in its own right. Instead, it often leads (once again) to the Pirc or Modern if White plays 2.e4, while 2.c4 will result in a King's Indian Defense or Old Indian Defense most of the time. It's not a particularly committal move, but it is one that's both flexible and strong.