I wouldn't recommend a gambit unless you are really dedicated to learning the lines, otherwise, any person, with at least some knowledge, will deconstruct you very easily.
I recommend the Queen's Gambit for white. Technically it's not a Gambit, however, it's still played very much at the GM level, and even at the low-level tiers, it's very powerful, as there ...
Many answers have already shown good examples, but I'd say that if you're looking for a sharp opening, you don't necessarily have to look for a gambit. In many occasions your opponent could refuse the gambit, or maybe give back the material and get a quieter position.
For example, as Black, you'll probably reach sharper positions by playing the Dragon ...
Two sound gambits for Black:
The Marshall Attack in the Spanish:
1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 Nf6 5. O-O Be7 6. Re1 b5 7. Bb3 O-O 8. c3 d5 9. exd5 Nxd5 10. Nxe5 Nxe5 11. Rxe5 c6 12. d4 Bd6 13. Re1 Qh4 14. g3 Qh3
This is the main line. Be aware that you need to know lots of theory to play this opening, as most lines are analysed ...
The Evans Gambit is probably one of the most sound. It's still occasionally played at GM level and most of the critical lines are rarely if ever tested.
The Vienna Gambit and Blackmar–Diemer are probably playable. The Scotch gambit is playable although I wouldn't be surprised if there isn't a forced draw.
With black the Benko is probably sound and the ...
You can have 'gambit', you can have 'sound', but you can't have both.... the Benko is the closest you're going to get. Take heart in the fact that gambits are perfectly OK in practice, if unsound in theory.
The Stafford is getting popular because of the Youtube videos I guess. I saw it earlier today and just played 5.Be2 to take it out of book and won easily.
It's a trappy opening and you're going to have to accept the fact that not every white move gives you a mate in 2.
The best move is probably Bf5. The downside to Qe2 is that 1) white hinders his own ...
Rats. I thought I had a 5. Qe2 somewhere... Crap, that colllection of Stafford games was on the stolen laptop.
...Bf5 was a suggestion earlier, right? Then if d3 kicks you back to c5, and d4 hits you again, you can drop back to e6 without blocking the bishop, or go in for ...Ne4 f3 Qh4+ Qf2 (what a mess) .
Chessplayers need to think of the opening more in terms of plans than in moves. Whether either the From or Lisitsin is good or bad, and any benefit from White's additional move in Lisitsin isn't as important as familiarity with this pattern:
rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1
1. g4 e5 2. f3 Qh4#
Oh, everyone ...
The Damiano Defense, also known as the five pawns gambit, is practically refuted. You can find the details on the Wikipedia page. The key line is:
e4 e5 2. Nf3 f6? 3. Nxe5! fxe5? 4. Qh5+ Ke7 5. Qxe5+ Kf7 6. Bc4+ d5 7. Bxd5+ Kg6 8. h4 h5 9. Bxb7
After which Black cannot stop Bxa8 with a decisive material advantage for White.
It's possible to keep the pawn but at the expense of seriously weakening the queenside and fall behind in development. Keeping the pawn is certainly playable but you will need to know how not to be busted in the centre.
Keeping or giving the pawn, both possible in Catalan. Whether you like it or not depend on your personal preference.
As a person who has experience in the Bird's and Dutch openings, I would say that both of them are somewhat bad responses to the Birds or Dutch. In the From's, generally white has the edge but its not as if black doesn't have counterplay. In the Lisitsin, usually something like 1Nf3 f5 2e4 fxe4 3Ng5 Nc6 4d3 e3 is something close to equal.
There is a version ...
You can try for Zukertort Trap in the Lisitsin Gambit line.
After 1. Nf3 f5 2. e4
the trap-line is Ng5
then if the opponent sticks with his pawn on f5, and pushes d5, then, simply play d3, followed by exd3 and then play Bxd3, and notice that the king has serious weakness on one of its diagonals.
Now, if opponent replies with Nf6, then the best option is Nxh7....