Nope. Photoshopped hoax. Correct 'future' date is October 21, 2015. http://www.snopes.com/inboxer/hoaxes/bttf.asp In the original movie though, he did start his time travel on my 34th birthday- October 26, 1985.
I think it's funny that this keeps making the rounds. I'm a bit of a fan of the Back to the Future trillogy, so I know it's not correct. Isn't it Bassic knowledge that the movie was set in 1985 and the future date was 30 years in the future? I don't want to blow my cover as a BTTF nerd, so I'll keep it at that. PS Marshall, that is a cool little piece of trivia.
"Nobody, calls me a nerd." LOL! My cover as a super fan of this trilogy was blown years ago! I know all three movies, line for line. "It is Wild Gunman. Watch out kid, I'm a crackshot at this." *sound effects "You mean you have to use your hands?! Thats like a baby's toy!" I can go on and on, and on. But I won't I'll bore you all. But seriously, look at everything in BTTF II in 2015. We won't have flying cars but a lot of the other stuff, at least the conecpts they were portraying have infact come true. Look Marty's future house. The printers in every room, the video chat, portable credit card scanners, all have either come true or the concept is here. With the printers in the walls of his house, the concept was that you were never "disconnected" and that no matter where you were, you knew what was going on. That was a prediction then, in the 1980s, and today it has come true with all of the technology we now have. Outside, you have the animated billboards, and the idea behind the Mr. Fusion - creating energy from household garbage.