Danish Gambit - 1.e4 e5 2.d4 exd4 3.c3 (focusing on lines that are independent of the Göring Gambit)
Urusov Gambit - 1.e4 e5 2.d4 exd4 3.Bc4 Nf6 4.Nf3 or 3.Nf3 Nf6 4.Bc4 (Note: here 4...Nc6 transposes to the Two Knights Defence; see Scotch Gambit lines with 4...Nf6)
Misc. move order issues:
Index of lines after 1.e4 e5 2.Nf3 Nc6 3.Bc4
Two Knights Defence: 3...Nf6 (here 4.d4 exd4 transposes into Scotch Gambit lines with 4...Nf6)
Italian Gambit: 3...Bc5 4.d4!? (4...exd4 transposes to the Scotch Gambit with 4...Bc5)
Evans Gambit: 3...Bc5 4.b4!?
Note: White can also try the Max Lange Gambit, 3...Bc5 4.0-0 Nf6 5.d4!?, which will lead to a Max Lange Attack after 5...exd4 6.e5 or, after 5...Bxd4 6.Nxd4 Nxd4, transpose into Italian Gambit lines following 4...Bxd4 5.Nxd4 Nxd4 6.0-0 Nf6. The main snag with this move-order is that Black can avoid the Max Lange Gambit with 4...d6. Then as Stefan Bücker and Lev Gutman pointed out in Kaissiber magazine, the immediate attacks with 5.d4 don't work very well, so White does best to go for a slow positional approach with c3, d3 and b4.
Also note: the old line 3...Bc5 4.c3 Nf6 5.d4 exd4, which is one that beginners often tend to learn, is covered via the Scotch Gambit with 4...Bc5 5.c3 Nf6.
Index of lines after 1.e4 e5 2.Nf3
2...f5?! - Latvian Gambit 2...d5?! - Elephant Gambit
Notes on the omission of the Vienna Gambit I haven't covered the Vienna Gambit (1.e4 e5 2.Nc3 intending 3.f4) because of the independent line 2...Nf6 3.f4 d5 (note that 3...exf4?! 4.e5 is bad for Black). Instead if 2...Nc6 3.f4, play often continues 3...exf4 4.Nf3 g5 transposing into lines covered via the Quaade Gambit with 4...Nc6. Instead 4.d4 is the Steinitz Gambit (covered via 1.e4 e5 2.f4 exf4 3.Nc3 Nc6 4.d4).
Other Misc 1.e4 e5 lines
White sacs a piece at move four... 2.Nf3 Nc6 3.Nc3 Nf6 4.Nxe5?! - Halloween Gambit 2.Nf3 Nf6 3.Nxe5 d6 4.Nxf7!? - Cochrane Gambit
There are a couple of Ruy Lopez lines that I intend to cover in the near future: Ruy Lopez (2.Nf3 Nc6 3.Bb5) 3...a6 4.Ba4 d6 5.0-0 Bg4 intending 6.h3 h5 - Yandemirov Gambit 3...a6 4.Ba4 d6 5.c3 f5 - Siesta Variation
White goes for the Scholar's Mate
I am yet to look into these lines yet, but I am interested in covering them in the near future. No doubt many players experimented with them when they first started out at chess, but didn't really know what they were doing beyond "try to checkmate on f7 with the bishop and queen". I certainly did... Also, Hikaru Nakamura famously experimented with 2.Qh5 at the grandmaster level. 1.e4 e5 2.Bc4 followed by 3.Qh5 1.e4 e5 2.Qh5 Nc6 1.e4 e5 2.Qh5 Nf6!?