Staying with Coral Sea - 2 votes to my mind less decisive than the Bismarck Sea.
Adding Cartegena des Indies - 2 votesfor the reasons stated by **merrick **above
and New Orleans - 1 vote another non-naval ‘battle’. The capture of New Orleans severely damaged the South’s cause but the war continued for another three years.
Sinking of the Repulse/Prince of Wales - 2
Bismarck Sea - 2
Falkland Islands in World War I - 1
Not a naval battle, hmm? Farragut probably thought differently at the time:
http://cache2.allpostersimages.com/p/LRG/29/2944/AZWRD00Z/posters/davidson-julian-oliver-capture-of-new-orleans-by-union-flag-officer-david-g-farragut-24-april-1862.jpg
http://www.history.navy.mil/photos/images/h42000/h42245.jpg
http://www.history.navy.mil/photos/images/h59000/h59071.jpg
http://www.springfieldmuseums.org/writable/collection/2004-D03-200.jpg
http://www.fineart-china.com/upload1/file-admin/images/new17/Mauritz%20F%20H%20Haas-899486.jpg
Noryang - 2
Bismarck Sea - 2
Ok…need a WWII Pacific battle to go 
so:
Bismarck Sea - 2
Coral Sea - 2 {looking at it I think Taranto makes the same case with more emphasis…but this is close - and even if the Japanese had won they didn’t have enough troops to take the objective IMO}
Cartagena de Indias - 1 so merrik doesn’t blow a gasket
Sinking of the Bismarck and the Prince of Wales - 2 for reasons given above.
Bismarck Sea - 2 for reasons given above.
Cartagena de Indias -1. I’ve got to agree with Merrick on this one. I see this as more of an amphibious assault than a true naval battle.
Repulse/Prince of Wales - 2
Cartegena de Indias - 1
Bismarck Sea - 1
Coral Sea 1
My understanding is that Farrugut had to get past the forts on the river to get up to the city. In this respect it’s like the Allied attempts to force the Dardanelles in WWI and Cartegena des Indies - a ‘fleet vs fort’ action.
Sorry - this is about the Batle of New Orleans
If you can’t convince 'em - intimidate 'em 
For the others, I’ll go with Bismarck Sea over Coral Sea & Force Z, simply for its small scale and lack of effect on the wider war.
Falkland Islands (1914) vs Noryang? Both were spectacular tactical victories with very little effect on the wider war (or on naval development in general). I’m also starting to think about Chesapeake (tactical draw), Lake Erie (famous but small-scale), Sluys, The Masts, The Yalu (even though I nominated it) and even the Glorious First. I’ll go with Noryang, on the grounds I hadn’t heard of it before this thread.
lisiate - I had New Orleans on my “not-a-naval-battle” list too, until I rembered the CSS Manassas. A footnote to history, as it turned out, but with a little more luck she could have taken the Virginia’s slot.
Cartagena de Indias : 2
Bismarck Sea : 2
Noryang : 1
Lol
I like the Masts because it gave Islam control over the North African coast and then into Spain. While not the most decisive in history…pretty important. Before then, the Arabs were a desert people who never had a fleet…then POOF. If not for a decisive land battle in France, Islam could have taken Europe though and end-run…all started pretty much with the Battle of the Masts.
6th Round round:
Bismarck Sea- 11
Sinking of the Repulse/Prince of Wales - 8
These 2 are eliminated.
Others got:
Coral Sea - 5
Cartagena de Indias - 5
Noryang - 2
Hansan - 1
New Orleans - 1
Falklands - 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.
Cape Bon ( 468 ) - Vandals destroy combined Roman fleet, nail in the coffin for the Western Empire.
Cartagena de Indias – British beaten by Spain in Colombia
Chesapeake: French defeat British; Cornwallis doomed
Coral Sea – Introduction of aircraft carriers facing each other
Diu: Portuguese smash the Ottoman/Mamluk/Indian fleet
The Downs - Larger Spanish fleet crushed, rise of Dutch dominance.
Falkland Islands in World War 1 seems pretty decisive.
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.
Lake Erie: Perry defeats British fleet; “We have met the enemy…”
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.
New Orleans: Farragut captures biggest Confederate city
Pearl Harbor - Japan is allowed to run amok and capture large amounts of territory
The Nile: strategically more important Napoleonic battle than Trafalgar
Noryang – Japanese invasions of Korea repelled
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
Round 7 due by say 2:00 Central Sunday. (3 days from now).
Noryang - 2
Cartagena De Indias - 2
Falklands - 1
Repeating last rounds votes (with a few more comments).
Coral Sea - 2 votes; quite close in terms of casualties, did not decide the Pacific War.
Cartegena de Indias - 2 votes; a failed amphibious assualt that didn’t decide the War for Jenkin’s Ear.
New Orleans - 1 vote; The presence of the CSS Manassas is not itself enough to transform this from a ship versus fort action to a true naval battle. (The actual occupation of the city is even less so).
Ah, but I nominated Noryang… 
Since it (along with Cartagena de Indias, another of my entrants) doesn’t appear long for the game anyway, I’ll stick with “protecting my own” for now, thus
Sticking with Hansan – 2
and adding
New Orleans – 2
Falklands – 1
Cartegena de Indias - 2
New Orleans - 2 It was an amphibious invasion, not a naval battle.
Lake Erie - 1 A notable victory, but did not directly influence the outcome of the War of 1812.
Cartagena de Indias is still in? Drat those meddling kids!
For the others, I’ll spread the love:
Noryang, for reasons already discussed; Lake Erie (spectacular, but a sideshow, and smaller in scale than most of the other) and for the last I’ll break new ground and toss in Yamen. It sounds impressive - the decisive defeat of the Song Dynasty and the triumph of Kublai Khan - but reading up it seems that the Song Dynasty haad been decisively defeated (on land) much earlier and Yamen was a matter of the Mongols mopping up the last hold-outs in their final offshore refuge. Even if the Song fleet had pulled a Salamis, what could they have achieved?
Cartagena de Indias: 2
Noryang: 1
Lake Erie: 1
Yamen: 1
Cartagena de Indias 2. For reasons given above. We’ve got to send some of these to Davy Jones’ locker.
Falkland Islands - 2. I can’t just see this as being that big a deal.
Cape Bon - 1. The Western Roman was going down no matter what happened at sea.
7th Round round: I added mine to results below.
Cartagena de Indias - 12
New Orleans - 5
Falklands - 5
These 3 are eliminated.
Others got:
Lake Erie - 3
Noryang - 3
Coral Sea - 3
Hansan - 2
Yeman - 1
Cape Bon - 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.
Cape Bon ( 468 ) - Vandals destroy combined Roman fleet, nail in the coffin for the Western Empire.
Chesapeake: French defeat British; Cornwallis doomed
Coral Sea – Introduction of aircraft carriers facing each other
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.
Lake Erie: Perry defeats British fleet; “We have met the enemy…”
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
Noryang – Japanese invasions of Korea repelled
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.
Round 8 due by say 2:00 Central Tuesday. (2 days from now).
Cape Bon – 2 for reasons I gave above.
Coral Sea – 2. We’ve got to toss out more of the Pacific battles.
Taranto – 1. More important for the fact that it demonstated it was possible to aerially launch torpedoes into shallow waters. This battle had a profound impact upon Japanesse thinking about Pearl Harbor, but I can’t see that it was that decisive.
Sticking with
Hansan – 2
Falklands – 2
and chiming in on
Cape Bon --1
You must really hate that battle, sticking with it after it was eliminated.