Comments:
1. e4 e5 2. Nf3 d6 3. Bc4
{Also, 3. d4 is a perfectly good move as well.}
3...Be6 4. d3 Bxc4 5. dxc4 Nf6 6. Bg5
{A tad aggressive, but the right idea. Personally, I'd go for 6. Nc3 first, and then 7. Bg5.}
6. ...h6 7. Bd2
{Honestly, take the knight. It's the only piece that can readily defend the hole on d5, and it's attacking your pawn on e4.}
7... Nxe4 8. Bb4
{What's the bishop doing out here? Castle, get your knight to d5 ASAP, and accept that you will eventually lose a not-so-useful
bishop.}
8... c5
{Now, the best spot for the bishop is on c3, hoping for 9.
...Nxc3 10. Nxc3.}
9. Nxe5 {??????? Now, you're simply giving Black a piece for free.}
9... cxb4 10. O-O
{You're knight on e5 is hanging. Simple as that.}
10... dxe5 11. Qxd8+ Kxd8 12. Rd1+ Nd7 13. c3 bxc3 14. bxc3 Rc8 15. Na3
{Hanging a third piece.}
15... Nxc3 16. Rd2 Bxa3 0-1
You will lose a lot of chess games if you give your opponent free pieces. Take the time to look at all your opponent's pieces, and check that the move you want to play doesn't give away material for free.