Planet of Evil shares some recognisable elements (most notably the possessed crewman with glowing eyes murdering their colleagues) with 42.
Planet of the Daleks had many bits that harked back to The Daleks.
Journey's End was in many ways a modern remake of The Five Doctors - with different groups of old characters being separately drawn into the story, then grouping together in a central location for the climax, whereupon they are all conveniently immobilised (by hypnosis or by force fields) so that the presence of too many characters doesn't overwhelm the writers.
The Bells of Saint John was The Idiot's Lantern for the twenty-first century.
Journey to the Centre of the TARDIS was cobbled together from the reheated leftovers of The Doctor's Wife.
The Runaway Bride had a lot of carry-overs from The Christmas Invasion.
Rise of the Cybermen tells a similar story to Genesis of the Daleks.
TV Tropes gives us a few more:
The Android Invasion and The Brain of Morbius
The Keys of Marinus and The Key to Time
Fear Her and Night Terrors
Victory had a lot of homages to Power and Evolution had many to Evil (of the Daleks).
The Curse of the Black Spot has the same reveal as The Doctor Dances.
The finale to Series 8 combines the finales of Series 2 and 3.
Heaven Sent shares some elements with The Deadly Assassin and Castrovalva, though I suppose all the Gallifrey stories will inevitably need some threads in common.
