The Danish Gambit is one of those daring 19th century openings that has inspired many amateur players. White gets a considerable lead in development at the cost of a couple of pawns.
In such cases Black must be careful, of course, but here I feel his task after accepting the offer is not difficult, since he has no structural weaknesses. His aim is to develop fast, and at the right moment return some material to get his own advantages. I will use three illustrative games (all won by white) to show that after Black's most natural move (5...Bb4+) White is nowhere close to achieving satisfactory compensation for his investment.
We start with the move 6.Kf1, which is considered in some sources the most promising for White: He simply gets his king out of the way to ensure his tactical tricks will work, and factly, he will be able to get back some material. But the mid-term problem with that move is the obstruction of the h1 rook, which Black can, with careful play, turn to his own advantage.
Meeting the check with 6.Nc3 is the most natural, and likely best move. However, this move does not hinder Black's development, who by natural means can get more than just a slight advantage.
Finally, we consider other white replies, but it's very difficult to find something particularly appetizing in them: White is clearly struggling.
Unless White manages to find some major improvement on those lines, his daring gambit should be rendered as completely unsound. Of course he may win the game, as happened here on all three games, but this cannot be done without generous cooperation by his opponent.
Perhaps White should consider using the Scotch Gambit move order to avoid the above continuation. However, things are not much more rosy- we will cover that possibility in the near future.