While it has been suggested that "the best way to refute a gambit is to accept it", there are those who prefer to go one step further, and offer their own aggressive gambit in turn.
Philidor1792 - Stranger
Casual Game, Chess-Samara.ru, 2014
1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6
About 4 years ago this blog discussed ways to approach this move (instead of 4...Bc5) in "Jerome Gambit vs Two Knights Defense" Parts 1, 2, 3, 4.
4.Bxf7+
As we have seen earlier in Philidor1792's play, after the alternative 4.Bb3 Bc5 5.Bxf7+ we would have a Delayed Jerome Gambit (see "Jerome Gambit-Inspired Play (Part 4)")
An early peek at this 4.Bxf7+ line occurred in "What's Going On Here?", and an early game was presented in "Opening Tale"; but much of what is in The Database on this line is from Philidor1792's games. (In some, below, he appears as "You".)
By the way, all of the referenced games can now be found in The Database.
4...Kxf7 5.Nxe5+
Some alternatives:
5.c3 Bc5 6.d4 in sTpny - yimansmellsbad, FICS, 2011 (0-1, 28);
5.Ng5+ in caovas - tomi36, 1 1 blitz, lichess.org, 2013 (1-0, 27) and KillerBishop - TheMentalist, 40 5, lichess.org, 2013 (0-1, 17);
5.d4 d5 (5...exd4 6.e5, yorgos - perrypawnpusher, blitz, FICS 2009, [1-0, 48]) in tomas2013 - tomi36, 1 2 blitz, lichess.org, 2013 (1-0, 22);
5.d3 d5 (5... d6 in viejoasquerosos - Killyourking, Redhotpawn.com, 2004 [0-1, 27]) cnselway - boycey, net-chess.com, 2001 (0-1, 11); and, finally
5.0-0 Bc5 6.Nc3, leobrazer - perrypawnpusher, blitz, FICS, 2009 (0-1, 48), transposes into a variation of the Italian Four Knights Jerome Gambit.
5...Nxe5 6.d4 Neg4
The alternative 6...Ng6 (met with 7.e5) was seen in Philidor1792 - Guest805466, 3 1 blitz, PlayChessBase.com, 2014 (1-0, 62); You-Stranger, blitz, Chess-Samara.ru, 2014 (1-0, 16)) You - Stranger, blitz, Chess-Samara.ru, 2014 (1-0, 17); Philidor1792 - guest1278, blitz, www.bereg.ru, 2014 (1-0, 29); Philidor1792 - Guest691264, 3 0 blitz, Play.ChessBase.com, 2014 (1-0, 14); and Philidor1792 - Juppzupp, 3 0 blitz, PlayChessBase.com, 2014 (1-0, 24).
Instead, 6...Nc6 (also met by 7.e5) was seen in Philidor1792 - guest345, blitz, www.bereg.ru, 2014 (1-0, 15); Philidor1792 - guest3018, blitz, www.bereg.ru, 2014 (½-½, 24); Philidor1792 - guest1334, blitz, www.bereg.ru, 2014 (1-0, 20); You - Stranger, blitz, Chess-Samara.ru, 2014 (1-0, 18); and Philidor1792 - Guest292640, 5 0 blitz, PlayChessBase.com, 2014 (1-0, 50).
Also seen was 6...Nc4 (also met with 7.e5) You - Stranger, blitz, Chess-Samara.ru, 2014 (1-0, 26).
7.e5 Nxf2
I hope Readers have stayed through all of the history and games above, as this game is about to get very violent. After all, Black has two extra pieces, and he can use them as he wishes.
8.Kxf2 Ne4+ 9.Ke1 Qh4+ 10.g3 Nxg3 11.Qf3+
11...Nf5+ 12.Kd1 g6 13.c3 Bh6 14.Bxh6 Qxh6 15.Nd2 Kg7
Black's counter-attack has slowed, but he still has the advantage - starting with a safer King.
16.Ne4 Ne3+ 17.Ke2 Rf8
At this point, Black's plans begin to go haywire - shortness of time?
18.Qxe3 Qxe3+ 19.Kxe3
The game is even - but not for long.
19...d5 20.Nf6 Bf5 21.Nxd5 Be4 22.Kxe4 c6
23.Nc7 g5 24.Nxa8 Rxa8 25.Rhf1 h5 26.Rf6 Rh8 27.Raf1 Black resigned
The good old Two Knights Defense.
Ha! says my opponent (in my imagination, anyhow). 
Transposing to a "modern" Jerome Gambit: 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kxf7 5.0-0 Nf6.
Move quickly, avoid a blunder, I have an extra piece...
Better 19...Bxb3. The clock is ticking down, but I have more time than my opponent, who now slips...
22.Re1 Re8 23.g3 Bd4 24.Rxe8+ Bxe8 25.Kg2 Bg6 26.Kf3 Bb1
There's enough time left for this to decide the game.