I have now completed the coverage of the 4.Ng5 lines in the Two Knights Defence. I don't expect this to be the last of my investigations into the Two Knights Defence as there is still the popular 4.d3 to look at (I am currently researching into 4...d5, the Chesspublishing.com suggestion of 4...Bc5 intending ...0-0 and only then ...d5, and Mark Nieuweboer's suggestion of 4...Be7 intending ...0-0, ...Ne8/Ng4 and ...f5) and the Boden-Kieseritzky Gambit may be worth giving some brief coverage to also.
The last three illustrative games cover the lines 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 d5 5.exd5 Na5 6.Bb5+ c6 7.dxc6 bxc6 and now 8.Bd3, 8.Be2 h6 9.Nh3, and 9.Nf3.
8.Bd3 is a tricky move which covers the e4-square and may envisage c2-c3 and Bd3-c2, tucking the bishop away, but Mark Ginsburg's recommendation 8...Ng4 looks strong against this, so I don't think there will be too many takers for 8.Bd3 over the coming decade.
8.Be2 h6 9.Nh3!? puts the knight on the rim and invites ...Bc8xh3, which I reckon will tempt most club players (it would certainly tempt me if I wasn't familiar with the line) but it is an error as White can shore up the kingside with Be2-f3-g2, or perhaps 0-0 and Kg1-g2, and enjoy the advantage of the bishop-pair. Instead Black should play around the knight on h3 and can expect to get full compensation for the pawn- indeed White often re-routes the knight back to f3 via g1 after a while.
9.Nf3 is the main move for White, after which play often continues with 9...e4 10.Ne5 Bd6 11.d4 exd3 12.Nxd3 Qc7.
I'm aware that there are authorities on the Two Knights Defence who are much higher-rated than I and who believe in Black's chances in this position but I personally think that after the strong plan with 13.b3 followed by Bb2, putting pressure on the black kingside, Black is struggling to maintain full compensation for the pawn.
But it may not matter, because the main alternative for Black, 10...Bc5, invites 11.c3 (threatening a pawn fork with b2-b4) and then Black continues with 11...Bd6, arguing that White's extra tempo with c2-c3 is harmful as it makes the plan with b2-b3 hard to engineer successfully. I think that after 10...Bc5, Black is having few problems demonstrating full compensation for the pawn (a view that has recently been shared by some of the regular contributors at Chesspublishing.com).
Thus, the 4.Ng5 lines with 4...d5 5.exd5 Na5 continue to look dynamically equal with best play, though of course at club level we often don't encounter best play. In my experience (having played both lines from the black side) the Ulvestad variation (5...b5), though less likely to provide full compensation for the pawn with best play, tends to be met less accurately than 5...Na5 at club level, so the choice between the two at club level is more a matter of taste and tolerance for risk, but at grandmaster level 5...Na5 is definitely the more reliable.
Finally, for further opinions on these lines, I refer readers to the section of Michael Goeller's bibliography on 1.e4 e5 2.Nf3 that he dubs the "Duffer's Attack", which covers each of the 4.Ng5 lines that I have recently investigated.
I have also updated the Scotch Gambit coverage (mainly just the format, and fixing the links from the main Two Knights page) for of course players of the Two Knights Defence need to have something ready against 4.d4, which after 4...exd4 transposes to the Scotch Gambit line 1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.Bc4 Nf6, which I have already looked at extensively.