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I once heard that you can sharpen your tactical skills by playing gambit openings? If this is true, obviously you would and should improve your game. Does anyone have any information or proof of this?

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IMO playing a gambit would increase your skill because you're taking a risk that could get yourself into a bad position or behind materially. This would lead to harder thinking and better tactical skills. –  Seth Jan 17 '13 at 20:17
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I think the goal is to play openings that lead to tactical positions, which is often achieved by playing tactical openings, of course. However, non-gambit openings can lead to tactical positions as well, for example playing open Sicilian is probably a better choice than playing Wing Gambit (1.e4 c5 2.b4). –  Akavall Jan 18 '13 at 0:27
    
I agree with Seth's comment. I sometimes play the King's Gambit to lead the game into tactically rich positions. (You might want to play it safe instead against more advanced players than you) –  retrodanny Jan 25 '13 at 16:31
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I think that there are important skills you can learn from playing gambits, like how to use an advantage in development and the initiative, or just the fact that material isn't everything. It's probably also useful to learn those things early on in your chess career.

I'm not sure about them being better for improving tactics though. Every chess game has tactics.

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Indeed, learning to part with material for minor and major positional advantages is a key in the recipe to learning to play on the "edge." In a gambit, the player who is ahead (gambitee) must eventually "give back" some material, otherwise risk getting in a loosing position. The player who is behind in material (gambiter) usually enjoys greater maneuverability and tactical lines.

It is the goal of the gambiter to not necessarily trade back for the loss of material, but to gain a better position or a strong attack. It is the goal of the gambitee to "give back" the material in such a way that he does not weaken his own position, preferably he can strengthen it. The outcome of the gambit is usually determined by how sound the gambit is and which player has more patient: the gambitee should not overextend to defend the material gain, the gambiter should not seek to immediately reclaim lost material.

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Why do you say "the player who is ahead (gambitee) must eventually "give back" some material" and "It is the goal of the gambitee to "give back" the material..."? It is fairly common that gambitee holds on the extra material, survives the attack, and gets to a winning endgame, and thus wins without ever giving back material. –  Akavall Jan 18 '13 at 0:20
    
It may be a personal observation, but rarely does a sound gambit end with a gimbitee winning endgame with the material they won. In such a case, I would label the gambit as unsound. –  ldog Jan 18 '13 at 1:27
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@Idog: I think sound gambits very often end that way. Soundness is a matter of how the game should end up theoretically, but in practice nobody is perfect and it's perfectly possible that the player with the extra material can hold on to it and win the endgame. I've won tens of Morra gambits as Black that way... –  RemcoGerlich Jan 18 '13 at 12:30
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