Previously I had just looked at the Fried Liver and Lolli Attacks (following 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 d5 5.exd5 and now the dubious 5...Nxd5, which allows White a choice between sacrificing on f7 immediately with 6.Nxf7, or deferring the sacrifice with 6.d4). For now, I maintain that 6.d4 is the more likely of the two to provide a theoretical edge, but that some players may well be better-served by 6.Nxf7, as it forces Black's king out into the middle of the board, and provided that White avoids the over-exuberant rook sacrifice with 6...Kxf7 7.Qf3+ Ke6 8.Nc3 Ncb4 9.a3?!, White should get enough compensation for the sacrificed knight (9.Qe4, 9.0-0 and 9.Bb3 are all good.)
However, Black has an interesting sideline at move 4, 4...Bc5!?, the Traxler Counterattack (Frank Marshall named this the Wilkes-Barre Variation, but this name has fallen largely into disuse as Traxler played the line many times before Marshall found out about it). It isn't as reliable as the main line with 4...d5 5.exd5 Na5, but following 5.d4 and 5.Bxf7+, Black gets a playable position, with partial compensation for the sacrificed pawn, while 5.Nxf7 Bxf2+, remarkably, appears to give Black enough of an attack for the material, even after going a rook and piece down in some cases, regardless of whether White plays 6.Kxf2 or 6.Kf1. The bad news for Black is that the line 6.Kxf2 Nxe4+ 7.Kg1 generally leads to a draw, although in practice White often goes wrong and loses.
For a second opinion there is Stefan Bucker's article, Seven Ways to Refute the Traxler. I broadly agree with his conclusions except that I think 5.Bxf7+ is about as good as 5.d4, and in my coverage at my site I have cited that article in numerous places.
The alternative approach to 4...d5 5.exd5 Na5 is to try 5...Nd4 (the Fritz Variation) or 5...b5 (the Ulvestad Variation). White's best bet against these is 5...Nd4 6.c3 b5 7.Bf1, or 5...b5 6.Bf1 Nd4 (6...h6 7.Nxf7 Kxf7 8.dxc6 is an interesting, but probably insufficient, alternative) 7.c3, transposing to the same position. Then after 7...Nxd5 8.Ne4, Hans Berliner's 8...Qh4 gives Black dangerous attacking chances but is theoretically somewhat dubious, but Black can get sufficient compensation for the pawn with 8...Ne6. Unfortunately for Black, after 8.cxd4 Qxg5 9.Bxb5+, as has been discussed a fair amount at the Chesspublishing.com forum, I don't think Black gets enough for the pawn. It's one of those, though, where at club level your chances of encountering a player who knows/finds this continuation, and knows what he/she is doing, is quite small, and White has a lot of inferior tries at move 6, especially after 5...b5.
I had one interesting encounter on the white side of the Traxler recently over at Chess.com. Although I won the game, Black had reasonable chances around the middle part of the game.
My next step will be to cover the important 4...d5 5.exd5 Na5 lines, which I think are fully sound.