It's kind of hard to choose between November 5 and November 12 of 1955. Of course, October 26 of 1985 is also an important day in BTTF history. Maybe November 5 of 1885, even though it's not really an important day for time travel - it's just an important day for the clock tower?
BTW, let's keep this to important dates within the BTTF Universe (in-universe) - so no saying things like July 3 of 1985, even though that was the day Part I was released (out-of-universe).
I would go with November 12, 1955. That's when Marty first went back to the future.
Well, there is certainly a lot of action that went on that day - not just in the way of time travel, but it's kind of a coincidence that the Enchantment Under the Sea Dance happens on the same night as the famous Hill Valley lightning. Do you think that night inherently contains some sort of cosmic significance, almost as if it were the junction point for the entire space-time continuum? Or do you think it could just be an amazing coincidence?
On a side note, I said that Doc's third child was a girl named Haven - and she was born at exactly 10:04 PM on November 12. In the Trilogy Universe, it was in 1986. In the Haven Universe, it was in 1985.
On the other hand, though, November 5 was the day that had started time travel (in meta-time, that is). It was the day that Doc had conceived the idea of the flux capacitor - and it's a coincidence that it happened to be the same day that George was hit by Sam Baines car (in the original timeline). Of course, in all subsequent timelines, that was the day that Marty showed up in 1955 and met both of his parents.
October 21 of 2015 is an important day, too - even though Doc has evidentally spent some time in the later days of that year. It was the day that could've ruined Marty's life. In Future History, it covers what Marty and Jennifer see - when they, once again, visit that day (through the natural course of time).
I don't really consider any day in 1885 to be quite as important as the Big Four (November 5 of 1955, November 12 of 1955, October 26 of 1985, and October 21 of 2015). Granted, there were a lot of important days in that year - but they just aren't quite as important.
Out of all three movies I would say November 12th 1955 because it is the night of the Enchantment Under the Sea dance, the clock tower getting struck by lighting, Marty being sent back to the future, and it is also very significant in Part II since it is when Old Biff gives his younger self the almanac and Marty and Doc go back to stop him.
That is the one date that you witness throughout the trilogy. There's even a little added scene in Part Three, when you see Marty carrying Doc into the mansion. Marty must be stronger than Michael J Fox - as they were neither Michael J Fox nor Christopher Lloyd.