Title   Existent   Owned
An unearthly child   yes   yes
The Daleks   yes   yes
The edge of destruction   yes   yes
Marco Polo   no   no
The keys of Marinus   yes   yes
The Aztecs   yes   yes
The sensorites   yes   no
The reign of terror   no   no
Planet of giants   yes   no
The Dalek invasion of Earth   yes   yes
The rescue   yes   no
The Romans   yes   no
The web planet   yes   no
The crusade   no   yes
The space museum   yes   no
The chase   yes   no
The time meddler   yes   no
Galaxy 4   no   no
Mission to the unknown   no   no
The myth makers   no   no
The Daleks' master plan   no   yes
The massacre of St. Bartholomew's eve   no   no
The ark   yes   no
The celestial toymaker   no   yes
The gunfighters   yes   yes
The savages   no   no
The war machines   yes   no
The smugglers   no   no
The tenth planet   no   no
The power of the Daleks   no   no
The Highlanders   no   no
The underwater menace   no   yes
The moonbase   no   yes
The Macra terror   no   no
The faceless ones   no   yes
The evil of the Daleks   no   yes
The tomb of the Cybermen   yes   yes
The abominable snowmen   no   yes
The ice warriors   no   no
The enemy of the world   yes   yes
The web of fear   no   yes
Fury from the deep   no   no
The wheel in space   no   yes
The dominators   yes   yes
The mind robber   yes   yes
The invasion   no   no
The Krotons   yes   no
The seeds of death   yes   yes
The space pirates   no   yes
The war games   yes   yes
Spearhead from space   yes   yes
Doctor Who and the Silurians   yes   yes
The ambassadors of death   yes   yes
Inferno   yes   yes
Terror of the Autons   yes   yes
The mind of evil   yes   yes
The claws of Axos   yes   yes
Colony in space   yes   yes
The daemons   yes   yes
Day of the daleks   yes   yes
The curse of Peladon   yes   yes
The sea devils   yes   yes
The mutants   yes   yes
The time monster   yes   yes
The three doctors   yes   yes
Carnival of monsters   yes   yes
Frontier in space   yes   yes
Planet of the daleks   yes   yes
The green death   yes   yes
The time warrior   yes   yes
Invasion of the dinosaurs   yes   yes
Death to the Daleks   yes   yes
The monster of Peladon   yes   yes
Planet of the spiders   yes   yes
Robot   yes   yes
The ark in space   yes   yes
The Sontaran experiment   yes   yes
Genesis of the Daleks   yes   yes
Revenge of the Cybermen   yes   yes
Terror of the Zygons   yes   no
Planet of evil   yes   no
Pyramids of Mars   yes   yes
The android invasion   yes   yes
The brain of Morbius   yes   no
The seeds of doom   yes   no
The masque of Mandragora   yes   no
The hand of fear   yes   no
The deadly assassin   yes   yes
The face of evil   yes   yes
The robots of death   yes   yes
The talons of Weng-Chiang   yes   yes
Horror of Fang rock   yes   yes
The invisible enemy   yes   yes
Image of the Fendahl   yes   yes
The sun makers   yes   yes
Underworld   yes   yes
The invasion of time   yes   yes
The Ribos operation   yes   no
The pirate planet   yes   no
The stones of blood   yes   no
The androids of Tara   yes   no
The power of Kroll   yes   no
The armageddon factor   yes   no
Destiny of the Daleks   yes   yes
City of death   yes   yes
The creature from the pit   yes   no
Nightmare of Eden   yes   yes
The horns of Nimon   yes   yes
Shada   no   no
The leisure hive   yes   yes
Meglos   yes   no
Full circle   yes   yes
State of decay   yes   yes
Warriors' gate   yes   yes
The keeper of Traken   yes   yes
Logopolis   yes   yes
Castrovalva   yes   yes
Four to doomsday   yes   yes
Kinda   yes   yes
The visitation   yes   yes
Black orchid   yes   yes
Earthshock   yes   yes
Time-flight   yes   yes
Arc of infinity   yes   yes
Snakedance   yes   yes
Mawdryn undead   yes   yes
Terminus   yes   yes
Enlightenment   yes   yes
The king's demons   yes   yes
The five doctors   yes   yes
Warriors of the deep   yes   yes
The awakening   yes   yes
Frontios   yes   yes
Resurrection of the Daleks   yes   yes
Planet of fire   yes   yes
The caves of Androzani   yes   yes
The twin dillema   yes   yes
Attack of the Cybermen   yes   yes
Vengeance on Varos   yes   yes
The mark of the Rani   yes   yes
The two doctors   yes   yes
Timelash   yes   yes
Revelation of the Daleks   yes   yes
The trial of a time lord   yes   yes
Time and the Rani   yes   yes
Paradise towers   yes   yes
Delta and the bannermen   yes   yes
Dragonfire   yes   yes
Remembrance of the Daleks   yes   yes
The happiness patrol   yes   yes
Silver nemesis   yes   yes
The greatest show in the galaxy   yes   yes
Battlefield   yes   yes
Ghost light   yes   yes
The curse of Fenric   yes   yes
Survival   yes   yes

So far I own 104 out of 129 complete serials, or 115 out of 156 incomplete/non-existent serials.

Existent in this context means the source material is both complete and available for release. Sadly, for many of the older Doctor Who serials this is not the case.
Trial of a timelord is listed as a single item rather than the 4 serials (The mysterious planet, Mindwarp, Terror of the Vervoids and The ultimate foe).
The owned, non-existent serials are all part of the Lost in time boxset.