The Morra (or Smith-Morra) Gambit against the Sicilian Defence runs 1.e4 c5 2.d4 cxd4 3.c3, though it is also sometimes reached via 2.Nf3 and then 3.d4 cxd4 4.c3, or 2.d4 cxd4 3.Nf3 and then 4.c3.
At my Gambiteers' Guild site I have finally completed an extensive coverage of Black's various defences in the accepted lines of the gambit. Each of the main lines contains discussion of a high-level practical example (indeed, each game has players rated no lower than 2295 Elo) and (and references to other examples in the notes) as well as analysis of alternatives for both sides.
It has proved to be a large undertaking, highlighting the issue that the Morra is not a good way of trying to avoid the heavy theory associated with various lines of the Open Sicilian (with Nf3, d4 and Nxd4). However, most club players should be able to get by with a working knowledge of the key ideas for White against Black's various defences, and if you know what you're doing you can pull off some fine attacking wins. As far as I'm aware, Black has at least a few defences that are sufficient to keep the game level with accurate play, but no refutations, and some of Black's more popular defences, such as the Classical Main Line with ...d6, ...e6 and ...e5, actually give White good chances of a theoretical edge, such as in this position, from G.Compagnone,G-R.Pietrocola, ICCF email 2011:
A key factor behind the recent revival of the gambit is the realisation that although in the lines with ...d6 and ...e6 with the black queen left on d8, White's best approach is a slow build-up starting with Qe2 and Rd1, against many of Black's other defences, White is advised to go for a more "gung-ho" approach, and should not be afraid to sacrifice further material in order to break through to Black's king, particularly the Nc3-d5 sacrifices. In some lines the Qe2, Rd1 approaches simply leave White a pawn down for not much.
Here are a few attractive piece sacrifices, which, to my knowledge, are not only 100% sound, but also represent best play for White in the following positions:
1) The Chicago Defence, 1.e4 c5 2.d4 cxd4 3.c3 dxc3 4.Nxc3 e6 5.Nf3 a6 6.Bc4 Nc6 7.0-0 d6 8.Qe2 b5 9.Bb3 Ra7 10.Rd1 Rd7 11.Be3 Nf6
12.Nxb5! (G.Souleidis-B.Kohlweyer, Germany 2000)
2) The early ...Nge7 defence: 1.e4 c5 2.d4 cxd4 3.c3 dxc3 4.Nxc3 Nc6 5.Nf3 e6 6.Bc4 a6 7.0-0 Nge7 8.Bg5 f6 9.Be3 Ng6 10.Bb3 b5
11.Nd5! (M.Esserman-L.Van Wely, Orlando 2011)
3) The early attempt to undermine White's e4-pawn by playing ...b7-b5-b4: 1.e4 c5 2.d4 cxd4 3.c3 dxc3 4.Nxc3 e6 5.Nf3 a6 6.Bc4 b5 7.Bb3 Bb7 8.0-0 b4
9.Nd5! (M.Esserman-J.Sarkar, Miami 2008)
Of course you have to take care when going all-out for glory like this - for instance, the Nd5 sacrifice tends not to be particularly sound when Black is only one move away from castling kingside (though even here, there are exceptions where White then gets a crushing kingside attack).
Black does have various ways of declining the gambit, including 3...Nf6, 3...d5 and 3...d3, and I intend to update my coverage of the gambit by discussing examples of these as well, as they are all frequently encountered in practice.