The 2nd Doctor

In The Power of the Daleks the Doctor gets used to his new body and his companions get used to him. An old enemy is uncovered on a colony world. At first Ben and Polly are sceptical that the new Doctor really is the Doctor, especially as he refers to the Doctor in the third person and he looks and acts completely different.

The Highlanders. The Doctor's introduced to Jamie McCrimmon

The Underwater Menace. The Doctor and Atlantis collide

The Moonbase.

The Macra Terror. Giant crabs menace a Terran colony

The Faceless Ones. Ben and Polly find they're back home and decide not to risk travellng further with the Doctor.

The Evil of the Daleks. The Doctor and Jamie gain a new companion; Victoria Waterfield and face an old enemy...

The Tombs of the Cybermen. ...then almost immediately face another.
This is Victoria's first proper adventure with the Doctor and she's dumped the Victorian dress to wear something more suitable for Carnaby Street 1960s style - presumably her own choice as Jamie's ideas of feminine deportment would be even stricter than her own and the Doctor has rarely been bothered by his companions' dress.
There are some seriously naff special effects particularly in the fight between Toberman and the cybercontroller.

The Abominable Snowmen. The companions are confronted by an alien intelligence in the high lands of Tibet.

The Ice Warriors.

The Enemy of the World. The Second Doctor bears an amazing resemblance to Salamander, who's trying to take control of the world

The Web of Fear. The Yeti are back, this time in the London Underground and the Doctor meets a man who will become a great friend.
Nick Courtney plays Colonel Lethbridge-Stewart and while UNIT does not exist at this stage, this story lays the foundations for those stories.

Fury from the Deep. After being attacked by giant seaweed, Victoria can't stand the thought of travelling with the Doctor any longer and decides that nineteen seventies Britain would be a safer place.

The Wheel in Space. The cybermen try attacking a tracking satellite and the TARDIS is invaded by a stowaway

The Dominators. Zoe's first proper adventure sees the companions visit the planet Dulkis, whose inhabitants had renounced violence and had no defences so when a passing starship stops off to refuel, the two Dominators aboard and their robots are able to intimidate the natives into acquiescing to their occupation. But what do the Dominators want with Dulkis?
Rather intriguingly, along with a completely hopeless fashion sense, the Dulcians have a pair of hearts to go along with their unwillingness to get involved...

The Mind Robber. When the TARDIS was forced outside Space-Time, the travellers find themselves in a strange land that responds to their very thoughts.
This is easily one of the trippier Doctor Who storylines.

The Invasion. The cybermen try yet another invasion of Earth...
By this story, Lethbridge-Stewart has the forces he wanted to counter the threat to Earth's security from 'unconventional sources' - UNIT has been born.

The Krotons.

The Seeds of Death. When the Martians decide that they need to invade Earth in order to survive, they realise that they will have to change the planet's atmosphere. Fortunately, Earth's transmat system is ideal for the purpose!

The Space Pirates.

The War Games. When the TARDIS lands the Doctor and his companions find themselves apparently on the Western Front in France; or is it Ancient Rome; or perhaps the American Civil War.... In order to untangle the confused time zones, the Doctor is forced to call in the Tine Lords of Galifrey, his own people. The Doctor is put on trial for gross interference with the Time Stream...

The Three Doctors. Taken out of his normal place in time by the Time Lords, the Second Doctor joins the First and Third in countering the effects of Omega. He is accompanied by Jamie.

The Five Doctors. The Second incarnation found himself involved with the other four early incarnations of the Doctor in order to overcome enemies on Gallifrey.
The Second Doctor is accompanied by the Brigadier having gone to his retirement bash.

The Two Doctors. When the Second Doctor is sent of a diplomatic mission to stop some time experiments, he is taken prisoner in order to provide some scientific materials...
The Doctor is travelling with Jamie during this story.