There have been a number of Doctor Who anniversary crossover-specials; to mark various anniversaries in the shows history.
There have been 5 to date :
1) The Three Doctors : 1973 – 10th Anniversary Special
2) The Five Doctors : 1983 – 20th Anniversary Special
3) The Two Doctors -1985
4) Remembrance Of The Daleks : 1988 – 25th Anniversary episode
They have on the whole – been a generally positive affair. Especially the Doctor crossover episodes – Two Doctors, Three Doctors and the Five Doctors.
These stories featured different combinations of Doctor incarnations, including :
1) The Three Doctors : 1973 featuring First, Second and Third Incarnations – William Hartnell, Patrick Troughton and Jon Pertwee.
2) The Five Doctors : 1983 – 20th Anniversary Special featuring First, Second, Third and Fifth Incarnations – William Hartnell, Patrick Troughton, Jon Pertwee, Tom Baker (in archive footage) and Peter Davison.
3) The Two Doctors -1985 featuring Second and Sixth Incarnations – Patrick Troughton and Colin Baker.
Crossover stories have always been problematic, in that they have to plausibly circumnavigate the First Law Of The Time – which states; “….no incarnation of a Timelord, will cross timelines with any other past or future incarnation.”
The specials found ways around this; however, including a devestating attack on Gallifrey – by previous Timelord founder Omega; from an anti-matter universe. Which prompt the Time Lords to call on the first Three Doctor’s – in The Three Doctors.
In The Five Doctors, four of the first five incarnations were successfully ‘time-scooped’ out of their timelines; by a forbidden Time Lord weapon.
In The Two Doctors, the Second and Sixth Doctors – are brought together merely by visiting the same space-station, during a similar time-period.
Remembrance Of The Daleks wasn’t a “physical” Doctor crossover story. Though it did include a backstory linking the First and Seventh incarnations, via the ‘hand of Omega’ Time Lord device. It also featured, the use of familiar locations from The Unearthly Child.
Dimensions In Time : 1993, was a short 30th Anniversary ‘Children In Need’ sketch featuring the Third, Fourth, Fifth, Sixth – and Seventh incarnations. In a bizarre short-sketch, featuring Eastenders cast and location.
The current Seventh Doctor, kept cycling back through each of his previous generations and various sets of companions and associated monsters. It wasn’t really canon, in the sense of the series – and was more for fun.
But it was interesting, seeing a crossover – featuring all of the ‘then’ incarnations, from number three, onwards.