The Doctor has met the same incarnation in:
- "The Big Bang" (11th Doctor)
- "Time" / "Space" (11th Doctor)
- "Last Night" (11th Doctor)
- "Journey to the Centre of the TARDIS" (11th Doctor)
For multi-Doctor stories:
- "The Three Doctors" (10th Anniversary) (1, 2, and 3)
- "The Five Doctors" (20th Anniversary) (1, 2, 3, and 5, with 4 out of the action)
- "The Two Doctors" (2 and 6)
- "Time Crash" (5 and 10)
- "The Day of the Doctor" (50th Anniversary) (10, 11 and "The War Doctor")
- "The Doctor Falls"-"Twice Upon a Time" (12 and 1)
Other occasions which might count are:
- "Logopolis", in which the 4th Doctor regenerates into the 5th with the help of "The Watcher", who's said to be the Doctor (the novelization expands on this a little)
- "The Ultimate Foe" (a.k.a "The Trial of a Timelord Parts 13 and 14"), in which the 6th Doctor meets the Valeyard, a dark version of the Doctor from between his twelfth and final incarnations
- "Journey's End", in which the 10th Doctor meets his meta-crisis half-human semi-clone
- "Amy's Choice", in which the 11th Doctor meets the Dream Lord, a manifestation of his dark side
- "The Almost People", in which the 11th Doctor meets a ganger of himself
- "Before the Flood", in which the 12th Doctor meets a hologram of himself
He's also seen, but not met, past versions of himself in:
- "Day of the Daleks" (3rd Doctor)
- "Father's Day" (9th Doctor)
- "The Wedding of River Song" (and "The Impossible Astronaut") (11th Doctor)
- "Before the Flood" (12th Doctor)
… and crossed his own timeline but avoided seeing himself in:
- "The Big Bang" (and the various episodes that he crossed in that story)
If you consider "Dimensions in Time" canonical, while he doesn't meet himself, he does change between his different incarnations.
Beyond the TV series, there are others; I won't attempt a complete list (especially counting the comics), but some examples are:
- "Cold Fusion" (Virgin Missing Adventures novel)
- "The Eight Doctors" (BBC Eighth Doctor Adventures novel)
- "The Sirens of Time" (Big Finish audio story) and "The Light at the End" (Big Finish audio story)
- In the Big Finish/AudioGO co-production series "Destiny of the Doctor", the Eleventh Doctor communicates directly with all of his previous selves, except the War Doctor.
There are even more novels, audios, and comics where he sees but doesn't interact with himself (e.g., when the 8th Doctor sees three visions of his possible next incarnation).
There's no reason the Doctor can't meet himself in the future. If they want him to meet _all_ of his past incarnations on TV, they'll have to use some tricks, because the first 3 actors (William Hartnell, Patrick Troughton, Jon Pertwee) have already died, and the 9th (Christopher Eccleston) is unwilling to return. But they've already used such tricks—Richard Hurndall played the 1st Doctor in "The Five Doctors", Jon Culshaw played the 4th in an audio story and recent audio dramas have had Peter Purves playing the First Doctor on a couple of occasions and David Troughton (son of Patrick) playing the 2nd Doctor too; both the 1st and 4th Doctors have also been represented by archive footage in previous multi-Doctor stories, while papier mache heads were used for the first 2 Doctors in "Dimensions in Time". It's unlikely any of these methods, however, would be acceptable to today's audiences on TV, and using CG to recreate the actors is too expensive for a BBC TV budget.
For further information, see List of multi-Doctor stories.