Which military battle in history do you think was the most famous or had the greatest impact?

While not technically battle, the atomic bombings of Hiroshima and Nagasaki clearly ended WWII and shaped the final half of the 20th Century.

A little known WWII battle, the Battle for Castle Itter, was a interesting one to say the least. This battle is the only known battle where American troops and German Army troops fought as allies. While I am sure there are other instances, however this one is documented in The Last Battle, by Stephen Harding.

I love history, especially history of conquest. To choose just one is impossible for me but I would have to say when the mighty Prussian Army was punished and beaten down in one single day by Napoleons Army, and yes I purposely state his Army as many of his men fought for him, not necessarily for France.
This changed the face of war and the face of Europe forever and I am actually partial to Prussia, having lived in the Prussian Headquarters "Berlin" for 15 years, I know the history well and know the Prussian Queens, Dukes and Duchess (there are so many it is incredible) I learned so much about Prussia (Preussen) that I fell in love with the history, the country of Germany and Europe in General.
I now live mostly in Budapest, the old Austro-Hungarian Empire territory, AND the Roman Empires farthest North Military instillation back in AD 106 time period, Caesar lived here for some time. The ruins are speckled throughout the city and along the Danube river, it is an incredible blessing to walk or drive through the city every day.
If you have never been, take a look at the skyline! (Sorry for highjacking the post!) CLICK ON THE PHOTO for the full panorama!

I think the most important battle in modern times was the Battle of Britain. If you look at it, Hitler had occupied much of Continental Europe (the parts that weren't neutral anyway) by mid-1940 and Great Britain was the only Allied power in the fight after France collapsed.

Nazi Germany had it all going for them; they had the numbers. Their pilots had seen more combat than the Brits. Germany also had massive amounts of troops prepared to land in the UK.

Britain was entirely on the defensive. They were outnumbered 10 to 1, but they had radar, which was relatively new. Radar enabled the Royal Air Force to vector fighter planes to locations ahead of a large group of enemy planes before they even arrived. Though they were outnumbered, these RAF pilots would pick off bombers and fighters, taking them by surprise and shooting many of them down before they could even reach England. While much of London was levelled to the ground, the damage was largely restricted to that area because Nazi planes couldn't breach British defenses deeper into England. With the help of American volunteers and joint units made up of Poles, French, Dutch, South African, Canadian, Australian and even New Zealanders, the numbers of pilots in the RAF increased. Had the RAF lost the war, British skies would have been open and the Germans would have been able to launch Operation Sea Lion, their offensive into the UK. Hitler decided to only send in the Luftwaffe first to soften up the RAF, which was a big mistake.

I have met numerous guys from the UK and they have all said that being a pilot in the RAF is a pretty prestigious thing. The struggle that RAF pilots faced during the summer of 1940 was great. They were facing a numerically superior force. With some radar and being in the right place at the right time, they turned the tables and made it impossible for Germany to ever have a hold over them again.