What is your favourite three battles and why

[MartinKnight1333]

For me Dunkirk 1940 is one, battered and surrounded but the rear guard did a fantastic job.
The other would be Waterloo, good choice of ground, well used and reserves in the right place.
The last Gettysburg, the high water mark where errors on both sides were made.

[FierceKitty]

Magnesia - two of the most spectacular armies ever, and it could have gone either way if the Hellenistic command had been up to the standard of even an average gamer.

Mikata ga Hara - must be the iconic battle for Sengoku enthusiasts.

Leuthen - if you need to ask, you won't understand the answer.

[Dr Dave]

"Favourite" is an understandable choice of word - but these are the ones that leave me most impressed, largely by the behaviour of those involved?

Barossa
Gettysburg
Arnhem

[Lord Kermit of Birkenhead]

No particular favorites, there is unfortunately too larger choice.

[petercooman]

Waterloo just a grand spectacle of uniforms!
Gettysburg intrigued by pickett's charge
D day landings, just the size of it all!

[Westmarcher]

Of course, Ian is right - there's just too many. But here are three of the many that stand out for me:-

Bannockburn, 1314.  Much to admire about what might be considered an unlikely victory by a greatly outnumbered, but probably better disciplined, medieval army with no heavy cavalry force to talk about. On the first day, the celebrated clash between Bruce and de Bohun when the latter spotted him in front of his troops and charged, lance couched. Bruce counter charged on his smaller horse, armed only with a battle-axe. What a risk - if he was killed that was surely game over. The effect on Scottish morale must have been tremendous. The following clash later that day when Randolph's schiltrom fought off the English heavy cavalry must also have given great encouragement to the rest of the Scottish army.  Then on the second day, instead of withdrawing, Bruce's outstanding generalship, having the courage to advance on the much larger English army and using the ground to hem it in and finish it off. 

Waterloo and Gettysburg are also favourites, no doubt reinforced by having personally visited each, the impressive supporting infrastructure for visitors at each site and the plethora of written and other historical resources associated with these two decisive battles.

[Norm]

Favourites and I can't even explain why;

Bosworth

Marengo

Hastings

[Raider4]

I assume you mean real? Then River Plate, the Battle of Britain and Agincourt.

If fictional is allowed, then Rorke's Drift (as per Zulu), Pelennor Fields (as per the book) and pretty much all of Red Storm Rising (the book).

[Ithoriel]

Field of the Gu'edina - first actual battle we know about

Kadesh - proof, should you need it, that Truth is the first casualty in war

Guadalcanal - land, sea, air, night raids, banzai charges, desperate defences, "Boys Own" levels of derring-do on both sides balanced by "Oops! I powered down 50% of our battleships in the middle of a fight, sir!"

[Duke Speedy of Leighton]

North Cape, the last battleship fight.
Mars-La-Tours, how to lose a war in an afternoon.
Shrewsbury, coz I used to live there...

[d_Guy]

Edgehill
Manassas(I)
Sedgemoor

(They share a similar theme)

Bonus:
Inverlochy (II) because - airing of grievances and feats of strength.

[steve_holmes_11]

Marathon:

Keep it simple, they don't like it up-em.
One of several battles to lend its name to a thing.
Also a battle that saved a civilisation.


Guldensporenslag or the Battle of Courtrai:

In which a bunch of butchers, bakers and candlestick-makers show a load of arrogant knights who's boss.
This marks the start of a few decades in which trained spearmen and archers came to recognise their power to resist.
Godentag invaders, we've come to eat fries and kick ass - however the potato hasn't yet been introduced.


The Battle of Britain

Unusual as a battle where all the action takes place in the air, with both sides developing best practice as they went along.
A great story with dashing heroes, and accessible history with the 5 phases of the German assault.
Also notable for the range of nationalities serving in the RAF
Remarkable engineering with the British Spitfire, Radar chain and communications network.
The Germans weren't too shabby either, but showed a few Achilles heels as the battle progressed.

[fsn]

Only three? Ohhhhh!

I've picked three-ish that are well know, but not famous. In the game show Pointless they would score somewhere between 1 and 20.

Salamis/Platea 480/479BC: Greece repels the Persian Empire - the finest moment of the Hoplite
Tours, 732: Charles Martel defeat the Arab invaders and arguably saves Western Christianity. 
Bannockburn, 1314: "Stitch that, Eddy!" One of the few times Scotland gets one over on England - and my daughter live there.
Maida, 1806; Sir John Stuart and a cute little action in Calabria. The British being confused by the red coats of the Swiss.
River Plate, 1939; The Graf Spee vs Exeter, Achilles and Ajax. the film (of the same name) was, and still is, one of my favourites. Also Matapan, 1941.

[GridGame]

Tsushima
Agincourt

[GridGame]

(Try again  )

Tsushima - 1st real ship-ship battle after sail. Also Japanese tactics and organisation resulted in a crushing victory: the result was the end of the war.
Agincourt - magnificent victory against the odds
2nd Battle of El Alamein - critical battle - what would have been the result if the Allies had not won?