I used to answer 1 d4 with 1...d5 or 1...f5. But in a couple of tournaments, I decided to try the Budapest Gambit, which I thought was unsound at the time.
It is not unsound. As a matter of fact, my opponents, when they were not busy avoiding my gambit with 1 d4 Nf6 2 Nf3 (which generally led to a Queen's Indian Defense), made a bizarre array of bad moves, hanging material and even getting mated quickly a couple of times.
As Moskalenko explains, the stem game of the Budapest was Adler-Maroczy, in 1896. After 1 d4 Nf6 2 c4 e5 3 dxe5 Ng4 4 Nf3 Bc5 5 e3 Nc6 6 Qd5 Qe7 7 Nc3 Nge5 8 Be2 d6 9 Ne4, Maroczy could have played 9...Nb4 with an excellent position. In fact, he played 9...Be6 and still won very quickly. In my first game with the Budapest, I played the same initial six moves as Maroczy. The game continued 7 e6 dxe6 8 Qh5 e5 9 Nc3 Nb4 and I won easily against a higher rated opponent. "How come everything is better than what I played?" she asked after the game.
In Adler's attack, a better line is 6 Nc3 O-O 7 Be2 Re8 8 O-O Nxe5 9 Nxe5 Nxe5 10 b3 a5 11 Bb2 Ra6. Yes, that piece on a6 is "Drimer's Rook," or as I call it, the "Budapest Castle." And Moskalenko shows us that once on a6, it tends to sail across the board to h6, where it threatens the White King. An example is 12 Ne4 Ba7 13 Qd5 Rh6 14 Bxe5 c6, which the author tells us about in detail.
I had always thought that Black would be in trouble if White played the following attack: 1 d4 Nf6 2 c4 e5 3 dxe5 Ng4 4 Bf4 Nc6 5 Nf3 Bb4+ 6 Nbd2 Qe7 7 e3 Ngxe5 8 Nxe5 Nxe5 9 Be2. But Moskalenko has some suggestions here, including 9...d6 10 O-O a5 11 Nb3 a4 12 a3 Bc3 13 bxc3 axb3, which I think is just fine for Black.
Of course, White can play 1 d4 Nf6 2 c4 e5 3 d5. Here, the author recommends 3...b5. I like this: we continue in the Hungarian tradition by switching to a sort of Benko Gambit!
In one of my Budapest games, White tried 1 d4 Nf6 2 c4 e5 3 dxe5 Ng4 4 Qd4 d6 5 exd6. Here, Moskalenko wants 5...Bxd6 (if 6 Qxg7? 6...Be5! wins for Black). But I played 5...Nc6 6 Qe4+ Be6 7 dxc7 (if 7 f3 Nf6 8 Qc2 Bxd6 9 e3, I think 9...Nb4 is good for Black) 7...Qd1+ (I found this move, which I called the "Jill Gambit," over the board in an earlier game, unable to resist the prospect of a family plan fork) 8 Kxd1 Nxf2+ 9 Kc2 Nb4+ (it's interesting to see how often Black plays 9...Nb4 in the Budapest) 10 Kb3 Nxe4 11 Nh3? a5! (this mate threat wins material) 12 Nc3? Nc5+ 13 Ka3 Nc2 mate.
In any case, this book is up-to-date and includes a great deal of explanatory material about strategies for both sides in this interesting gambit. I highly recommend it.