4. Blast From The Past
Two worlds collided in the 2007 Children in Need special Time Crash when the Tenth and then current Doctor somehow fused his TARDIS with the Fifth Doctor's which caused both of them to come together in one console room. The Fifth Doctor initially assumed that his future incarnation was a fan who had somehow broken into the TARDIS. Whilst trying to avert a black hole paradox, the Fifth Doctor is annoyed that his future self seems to be generally nonchalant about the impending doom. He finally realises what's going on when the Tenth Doctor casually sets off a supernova and his predecessor realises that he remembers himself doing it (or something timey-wimey like that). After some "fanboying" (admittedly it's mostly from the Tenth Doctor), they go their separate ways. It was an iconic meeting that fans will always remember.