After watching "The Day of the Doctor", I am trying to categorize how many Doctors were in the episode. Since this involves spoilers, I will put it behind a cut:
So we have Matt Smith and David Tennant playing the Doctor, this much is clear. So at the very least we have a dual-Doctor episode. We then have John Hurt playing the War Doctor. Some people might not consider this a Doctor, since he was only introduced for this this episode. But we can probably call this three. We then have Peter Capaldi in a three second, silent cameo. He is definitely a Doctor, but some might consider the briefness of his appearance to be disqualifying. And then we have Tom Baker, who was maybe or maybe not playing a Doctor. But who was certainly an actor who played the Doctor. Then we have archival footage.
So depending on how you look at it, we have 2,3,4,5 or many Doctors present in this episode.