I play the Italian Game OTB religiously, and have seen practically every response to 3. Bc4. While some are complete rubbish (3... Na5? 4. Nxe5 Nxc4 5. Nxc4) there are one or two that require pondering over. It is these that we will look at today.
First off, what does this move actually achieve? It is a step towards castling, and might defend against a Bg5 pin if (when) the knight comes to f6. Other than that, however, it is a completely defensive move that creates no threat in particular- therefore, the simplest response is to just play to opening principle. The best move here is (I believe) 4. d4, similar to a scotch game but with the bishops developed.
This move seems to me a little anti-developmental, but I see it a fair number of times. While it may open lines for black's white-squared bishop, at the same time it blocks lines for his black-squared counterpart. It overdefends e4, which we weren't going to attack anyway. So, it looks like a pretty silly move. Unfortunately, black will probably be able to equalise in this line.
This is probably the worst of the three moves we are looking at. It is played usually by weaker players who are afraid of 3... Nf6 4. Ng5. However, it fails to actually achieve anything. White should have no problem gaining an advantage in this line.
And there we are. Three uncommon (though not dismissable) moves in reply to the Italian Game. Unfortunately, we can do little more than gain a slight advantage against our opponents in such opening lines- it is up to the player to convert it into a win!