I have played chess seriously for a little over a year and my style is an aggressive one. I started off playing really dubious gambits (at least in my opinion) like the King's Gambit and the Latvian Gambit, immediately looking to give away material for active play right from the opening. I have since toned down my aggressiveness, preferring much more quiet openings like the Ruy Lopez and the Pirc. I really want to re-ignite my gambit play and I need some suggestions on sound gambits I could go for and why.
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 Budapest is playable. Black has fewer sound gambit options since black starts out a half tempo down. Giving up a pawn for a move just gives you an equal position but you're down a pawn.
I'll add though that virtually any opening is playable below 2000 level and certainly in rapid or blitz. In fact, you could probably get to around 2300 with any normal openings.
Two sound gambits for Black:
The Marshall Attack in the Spanish:
[fen ""] 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 well into endgames and play is concrete enough to grant an advantage to the one who knows more. Also White can avoid it and play Anti-Marshall lines.
Another gambit for Black stems from the Ng5 Italian
[fen ""] 1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 d5 5. exd5 Na5 6. Bb5+ c6 7. dxc6 bxc6 8. Be2 (8. Bd3 Nd5) h6 9. Nf3 (9. Nh3) e4 10. Ne5 Bd6
Where Black gives a pawn and accepts an inferior pawn structure for a lead in development and a strong initiative. I have to admit I did not believe this can be sound, especially given how chaotic Black's position is, but then I looked at theory and was very amazed how much Black gets and how little the structure matters in what is to come. Both sides need to know what they are doing or the game will be decided very fast.
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 Sicilian against e4 and the Benoni or Grünfeld against d4 than by playing gambits.
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 are a couple of nasty traps you can learn.
FOr Black, I would recommend the Sicilian Opening. I know its not a Gambit, but the Hyper-Accelerated Dragon is a very lethal weapon in the hands of an experienced player, and it is very aggressive, leading to very open positions, and often relying upon lethal forks and pins to shut down whites chances early