OK. Mission 1 accomplished 
Now I have to think. Actually, no I don’t I still have three left from last round:
2 - Noryang (if we have too many Pacific War battles, we have way too many Imjin War battles)
2 - Lake Erie (really a sideshow compared to most of the others on the list)
1 - Yamen (a foregone conclusion, and failed to make the Mongols/Yuan notably naval-minded)
Noryang - 2
Lake Erie - 2
Staying with Coral Sea for 2 points.
Adding
Lake Erie - 2 points a fine result but not significant enough to my mind.
Noryang - 1 point, I really need to read up on the Imjin war but agree that there’s no way that so many of its actions belong here.
Oooh, I seem to have missed a bunch of rounds.
I’ll vote for:
Lake Erie (2 votes) - While decisive in the sense of immediate, smashing victory of one force over the other, not really long-term decisive in the sense of changing the course of history. The War of 1812 just wasn’t made for dramatic changes in the course of world history.
The Yalu (1 vote) - In retrospect pretty clearly an impressive Japanese victory, but at the time the Japanese were badly damaged enough to cede the battlefield to the Chinese, and the ultimate destruction of the Chinese fleet would have to wait for the near future. Japanese successes on land also made the naval victories less important to the course of the war.
Coral Sea (1 vote) - neat introduction of carrier vs. carrier combat, but that was inevitable given the successes of carriers at Taranto and Pearl Harbor. The battle itself is overrated as having an influence on the course of the war, and the tactical result was pretty close to a draw.
Cape Bon (1 vote) - I kind of feel like I shouldn’t vote for it, because I don’t know much about it. Just hoping to spark some discussion of it.
8th Round round: I added mine to results below.
Lake Erie - 10
Cape Bon - 5
Noryang - 5
Coral Sea - 5
These 4 are eliminated.
Others got:
Hansan - 2
Yeman - 1
Taranto - 1
The Yalu - 1
Remaining:
Actium - Octavian defeats Mark Antony; takes Roman Empire.
Battle of the Aegates Islands – Rome ends 23-year First Punic War, assumes lasting naval dominance
Aegospotami - Lysander’s destruction of the Athenian navy finished the Athenian Empire.
Black May-when the Western Allies got the upper hand against the u-boats for good.
Chesapeake: French defeat British; Cornwallis doomed
Diu: Portuguese smash the Ottoman/Mamluk/Indian fleet
The Downs - Larger Spanish fleet crushed, rise of Dutch dominance.
Glorious First of June: Decisive British win over French
Gravelins: Spanish Armada turned back by England to meet their famous fate.
Hansan - Brilliant maneuvering leads to key victory in Imjin War.
Jutland During WWI- Germany effectively neutralized.
Lepanto: Ottoman high water (heh) mark
Leyte Gulf: Swan song for Imperial Japan
Manila Bay – Led to Dewey being given the unique (at least for USA) honor of Admiral of the Navy
Marmara (677) - Greek Fire stopped the Arabs outside Constantinople - and the Byzantines would roadblock Islam for another 700 years.
The Masts - Arabs/Islam take to the sea and kick Byzantium butt.
Midway: U.S ambushes Japanese fleet
Myeongnyang - Shattered remnants of Korean fleet holds off and smashes a massively larger Japanese invasion fleet.
Pearl Harbor - Japan is allowed to run amok and capture large amounts of territory
The Nile: strategically more important Napoleonic battle than Trafalgar
The Battle of the Philippine Sea - aka The Great Marianas Turkey Shoot - The USN destroyed the remnants of the IJN carrier force.
Quiberon Bay - the cherry on the Year of Victory, it secured control over the Atlantic for Britain and doomed French Canada.
Salamis: Greeks turned back Persian fleet
Sluys - Massive French invasion fleet annihilated, preempting a descent on England.
Second Battle of Syracuse/Sicilian Expedition – Athenian expedition cut off/wiped out.
Taranto: ascendancy of the airplane over the “fleet in being” (even more notable considering the small, weak, obsolescent air units involved)
Trafalgar: Brits won against France/Spain in Nap.war
Tsushima - Japan annihilates the Russian fleet
The Yalu - Japan’s victory was the start of Japanese imperial expansion, and a death blow to the Qing Empire.
Yamen – Mongol-controlled Yuan Dynasty crushed Song Dynasty in China
Eliminated:
Sinking of the Lusitania – One sided, but helped doom the Germans in the big picture.
Kamikazi “divine winds” origin – Mongol invasion of Japan fails due to typhoon
H.L. Hunley sinking the Housatonic - The first submarine to sink an enemy vessel.
Baltimore - AKA the attack on Fort McHenry
Flamborough Head – I have not yet begun to fight!
The sinking of the INS Eilat, 1967 - the first battle vessel sunk using ship-to-ship missiles.
Denmark Strait - The Bismarck and the Prinz Eugen of Germany meet the Prince of Wales and the Hood of Britain.
Hampton Roads: USS Monitor vs. CSS Virginia - first ironclad duel
Operation Dynamo – Evacuation of Dunkirk allowed the Allies to live to fight another day
Bismarck Sea: The Cannae of airpower vs naval power
Sinking of Prince of Wales and Repulse - The blow from which the British Empire never recovered
Cartagena de Indias – British beaten by Spain in Colombia
New Orleans: Farragut captures biggest Confederate city
Falkland Islands in World War 1 seems pretty decisive.
Lake Erie: Perry defeats British fleet; “We have met the enemy…”
Cape Bon ( 468 ) - Vandals destroy combined Roman fleet, nail in the coffin for the Western Empire.
Noryang – Japanese invasions of Korea repelled
Coral Sea – Introduction of aircraft carriers facing each other
Round 9 due by say 2:00 Central Thursday. (2 days from now).
Going to go first this time 
Jutland - 2
The Battle of the Philippine Sea - 2
The Yalu - 1
Making sure not to vote for the Falklands this time, I’ll stick with
Hansan – 2
and add
The Battle of the Philippine Sea – 2
Quiberon Bay – 1
Just to keep things different, I’ll go for:
Yamen - 2 (as mentioned earlier, it was basically finishing off a war that had already been won on land, and led to nothing very significant in the terms of wider naval development)
Taranto - 2 (surprised to see this one still in; a great achievement but didn’t greatly affect the wider war nor had much of an effect on naval development - Pearl Harbour would have happened regardless of Taranto)
Manila Bay - 1 (can’t argue with the decisiveness of the outcome, but again it was a relatively small-scale action, in a minor theatre, and the Spanish fleet was a busted flush.)
Blinking Duck & Sternvogel - why the Philippine Sea before Leyte? Sure, Leyte was bigger (due to the larger US fleet), but the ratio of forces was far more one-sided. And you can hardly argue that it was less decisive, since the destruction of Japan’s remaining naval aviation ensured that the Japanese fleet would spend the rest of the war in the role of targets. Leyte, like Yamen, was a killer blow in a fight already won - and without the Philippine Sea there would have been no Leyte, since the US could never have launched the Philippine invasion with an effective Japanese carrier fleet to oppose them.
Before the Philippine Sea, the Japanese thought they could win a major fleet engagement (and actually broke off potentially-successful operations elsewhere to fight one). Before Leyte, they had been reduced to desperation shots.
And I’ll speak up for Quiberon Bay, since I nominated it. Or rather, I’ll let Mahan do it for me: “The battle of 20 November 1759 was the Trafalgar of this war”. At the start of the year, the French were seriously planning an invasion of England. By the end, France’s fleet was broken, France’s colonies were defenceless and France’s creditors were foreclosing on their loans.
Merrick - Leyte is on my short list also. I think both battles, while huge, were not hugely decisive. Japan was toast already.
We not getting many responders. Will extend by 1 day to see.
That’s what y’all get for voting out Operation: Dynamo so early. 
Yamen - 1
Taranto - 1
Philippine Sea - 1
Black May - 1
Hm. I’ll vote for:
Coral Sea - 2 votes
The Yalu - 1 vote
Manila Bay - 1 vote (finding merrick’s comments persuasive)
Jutland - 1 vote (meant to be the decisive naval battle by both sides, but thanks to superb positioning by Jellicoe and a well-executed 180° by Scheer, pretty much returned things to the status quo ante. True, the German fleet only sortied briefly after Jutland, but it was never in the position where it could have broken the Allied blockade anyway.)
Hey! Did you see me cast even 1 vote for Dynamo? huh? huh!!?
Manila Bay – 2. I agree with Merrick.
Leyte Gulf – 2. We’ve got to get rid of more of these Pacific War battles, and I don’t think this was as important as the Great Marianas Turkey Shoot and Midway.
Taranto – 1. For reason I gave above.
9th Round round:
The Battle of the Philippine Sea - 5
Taranto - 4
Manila Bay - 4
These 3 are eliminated.
Others got:
Jutland - 3
Yeman - 3
The Yalu - 2
Hansan - 2
Leyte - 2
Black May - 1
Remaining:
Actium - Octavian defeats Mark Antony; takes Roman Empire.
Battle of the Aegates Islands – Rome ends 23-year First Punic War, assumes lasting naval dominance
Aegospotami - Lysander’s destruction of the Athenian navy finished the Athenian Empire.
Black May-when the Western Allies got the upper hand against the u-boats for good.
Chesapeake: French defeat British; Cornwallis doomed
Diu: Portuguese smash the Ottoman/Mamluk/Indian fleet
The Downs - Larger Spanish fleet crushed, rise of Dutch dominance.
Glorious First of June: Decisive British win over French
Gravelins: Spanish Armada turned back by England to meet their famous fate.
Hansan - Brilliant maneuvering leads to key victory in Imjin War.
Jutland During WWI- Germany effectively neutralized.
Lepanto: Ottoman high water (heh) mark
Leyte Gulf: Swan song for Imperial Japan
Marmara (677) - Greek Fire stopped the Arabs outside Constantinople - and the Byzantines would roadblock Islam for another 700 years.
The Masts - Arabs/Islam take to the sea and kick Byzantium butt.
Midway: U.S ambushes Japanese fleet
Myeongnyang - Shattered remnants of Korean fleet holds off and smashes a massively larger Japanese invasion fleet.
Pearl Harbor - Japan is allowed to run amok and capture large amounts of territory
The Nile: strategically more important Napoleonic battle than Trafalgar
Quiberon Bay - the cherry on the Year of Victory, it secured control over the Atlantic for Britain and doomed French Canada.
Salamis: Greeks turned back Persian fleet
Sluys - Massive French invasion fleet annihilated, preempting a descent on England.
Second Battle of Syracuse/Sicilian Expedition – Athenian expedition cut off/wiped out.
Trafalgar: Brits won against France/Spain in Nap.war
Tsushima - Japan annihilates the Russian fleet
The Yalu - Japan’s victory was the start of Japanese imperial expansion, and a death blow to the Qing Empire.
Yamen – Mongol-controlled Yuan Dynasty crushed Song Dynasty in China
Eliminated:
Sinking of the Lusitania – One sided, but helped doom the Germans in the big picture.
Kamikazi “divine winds” origin – Mongol invasion of Japan fails due to typhoon
H.L. Hunley sinking the Housatonic - The first submarine to sink an enemy vessel.
Baltimore - AKA the attack on Fort McHenry
Flamborough Head – I have not yet begun to fight!
The sinking of the INS Eilat, 1967 - the first battle vessel sunk using ship-to-ship missiles.
Denmark Strait - The Bismarck and the Prinz Eugen of Germany meet the Prince of Wales and the Hood of Britain.
Hampton Roads: USS Monitor vs. CSS Virginia - first ironclad duel
Operation Dynamo – Evacuation of Dunkirk allowed the Allies to live to fight another day
Bismarck Sea: The Cannae of airpower vs naval power
Sinking of Prince of Wales and Repulse - The blow from which the British Empire never recovered
Cartagena de Indias – British beaten by Spain in Colombia
New Orleans: Farragut captures biggest Confederate city
Falkland Islands in World War 1 seems pretty decisive.
Lake Erie: Perry defeats British fleet; “We have met the enemy…”
Cape Bon ( 468 ) - Vandals destroy combined Roman fleet, nail in the coffin for the Western Empire.
Noryang – Japanese invasions of Korea repelled
Coral Sea – Introduction of aircraft carriers facing each other
The Battle of the Philippine Sea - aka The Great Marianas Turkey Shoot - The USN destroyed the remnants of the IJN carrier force.
Taranto: ascendancy of the airplane over the “fleet in being” (even more notable considering the small, weak, obsolescent air units involved)
Manila Bay – Led to Dewey being given the unique (at least for USA) honor of Admiral of the Navy
Round 10 due by say 2:00 Central Weds. (3 days from now).
Sticking with:
Hansan – 2
Quiberon Bay (which got left out of the last round’s tabulation) – 2
Adding:
Leyte Gulf – 1
Denmark Strait - 2 - yeah, it was a victory, but in the grand scheme of things, it did not affect the outcome of the Battle of the Atlantic. By this point, it was going to come down to the U-Boats versus the Escorts.
Leyte - 2 - Japan was defeated at this point, it was just a question of “When?” rather than “If?”
Quiberon Bay - 1 Just another in a long line of French defeats versus the Royal Navy.
Gonna vote for:
Coral Sea 2 votes
The Yalu 2 votes
and, realizing that I shouldn’t vote for Jutland while Leyte Gulf is still on the list
Leyte Gulf 1 vote
Wow, had to do a lot of reading on some of these, especially the Asian ones.
Having read up on Hansan, I’m shocked to see any votes to remove it at this point. The Koreans were outnumbered and annihilated the Japanese. The Wikipedia page seems to have a bit of trouble with consistency in numbers, but claims that either 47 Japanese ships were destroyed and 12 captured, or 66 destroyed, out of 73 – while no Korean ships were lost; the casualty list is 9000 to 133, AND it crippled the Japanese invasion of China, saving the Ming dynasty, AND the Korean admiral introduced a new tactic (“crane wing”) based on new technology (cannons). It seems to be positively bristling with criteria for decisiveness.
The same cannot be said of the battles starting with Y. Yamen is plagued by uncertain numbers and seems to have involved a lot of noncombatants, and marked the last gasp of an already-beaten dynasty in flight. Yalu, much later (the pre-dreadnought era) did see one side suffer substantial ship losses, but that side (the Chinese) successfully carried out the amphibious landing they were protecting, and their enemy withdrew. The war was decided on land anyway.
I’m also throwing Quiberon Bay in there. The Wikipedia article displays outstanding confusion as to the losses:
[QUOTE=Wikipedia]
The British Admiral Sir Edward Hawke with 23 ships of the line caught up with a French fleet with 21 ships of the line under Marshal de Conflans and, after hard fighting, sank, captured, or forced aground most of them
[/QUOTE]
but lists French losses thusly:
6 wrecked/destroyed
1 captured
If 7 is “most” of 21, I’m bad at math. Furthermore, in the order of battle section, it’s revealed that a lot of the ships ran aground, or in one case, a ship was mysteriously “lost.” The battle is credited with determining the fate of New France in the New World, I suppose on the presumption that, had they not lost control of the seas, the French could have dramatically reversed their colonization policy and massively reinforced New France in ways they never showed any interest in otherwise, but that seems pretty speculative.
Jutland’s on my short list too, but I’ll hold my fire for now.
Yalu - 2
Yamen - 2
Quiberon Bay - 1