The First Doctor encounters himself in the story The Space Museum (albeit frozen and as an exhibit), the Third Doctor encounters and interacts with himself in the story Day of the Daleks, the Fourth Doctor encounters and interacts with the future incarnation of himself (the 'Watcher') in the story Logopolis, the Ninth Doctor observes a former version of his current incarnation in "Father's Day", and the Eleventh Doctor briefly comes face to face with himself in "The Big Bang".
In which episode does the First Doctor see himself?
The Space Museum