In the original series, the Third Incarnation of the Doctor accidentally phased himself into a parallel world which just might have been the legendary "Evil Mirror Universe" of 'Star Trek' fame. (This happened during the story "Inferno'.)
And in both of those dimensions, even though they met alternate versions of friends, there was no doppelganger of the Doctor around.
As stated in 'Lost', the Universe always has to course-correct itself, and this could be why the Doctor never met "Himself" when in an alternate dimension. The other TV dimensions probably couldn't handle more than one version of any particular Time Lord at a time.
So - just like in the 'Star Trek' episode "Mirror, Mirror" - as one Doctor crossed over into a different dimension, the doppelganger crossed over to the main Toobworld.
(As for when several Incarnations of the Doctor from Earth Prime-Time have met each other, it has always been under extenuating circumstances - problems with the TARDIS, anti-matter universes, pocket dimensions outside of Time.... Granted, I don't have any real splainin for what happened in "The Two Doctors".....)
But these kinds of Doctoral pairings shouldn't happen unless the circumstances are exact:
I've already posted earlier today about another time when the Doctor may have crossed over into another Dimension - that of the world without Holmes. I've got theories about what happened to those other two alternate Doctors when they arrived over in Earth Prime-Time, so I'll still need to figure out where that other Doctor ended up in the main Toobworld if I'm to keep the theory valid.
Stay tuned - the next three entries will be about the Doctors you only think you've never met!