I want to watch important episodes as well!
Ok. I don't know what's available to stream, but here's a list of episodes that are either good, or important for reasons of lore, regeneration or companion leaving/joining:
Hartnell:
Unearthly Child(just episode 1)
The Daleks
The Edge of Destruction
The Aztecs
Planet of Giants
The Dalek Invasion of Earth
The Rescue
The Romans
The Chase
The Time Meddler
The War Machines
The Tenth Planet
Troughton
Tomb of the Cybermen
The Ice Warriors
The Enemy of the World
The Web of Fear (probably, haven't seen this yet - awaiting the dvd)
The Mind Robber
The Invasion
The Seeds of Death
The War Games
Pertwee
Spearhead from Space
Doctor Who and the Silurians
Ambassadors of Death
Inferno
Terror of the Autons
Day of the Daleks (special edition dvd version is much better)
The Sea Devils
The Time Monster
The Three Doctors
Carnival of Monsters
The Green Death
The Time Warrior
Planet of the Spiders
T Baker
Robot
The Ark in Space
Genesis of the Daleks
Terror of the Zygons
Pyramids of Mars
The Brain of Morbius
The Seeds of Doom
The Masque of Mandragora
The Hand of Fear
The Deadly Assassin
The Face of Evil
The Robots of Death
The Talons of Weng-Chiang
Horror of Fang Rock
The Invisible Enemy
The Invasion of Time
The Ribos Operation
The Stones of Blood
The Androids of Tara
City of Death
Full Circle
State of Decay
Warriors’ Gate
The Keeper of Traken
Logopolis
Davison
Castrovalva
Kinda
Earthshock
Arc of Infinity
Mawdryn Undead
Enlightenment
Resurrection of the Daleks
The Five Doctors
Planet of Fire
The Caves of Androzani
C Baker
The Twin Dilemma
Vengeance on Varos
The Mark of the Rani
The Two Doctors
Trial of a Timelord
Mccoy
Time and the Rani
Dragonfire
Remembrance of the Daleks
The Happiness Patrol
The Greatest Show in the Galaxy
Battlefield
Ghost Light
The Curse of Fenric (dvd special edition version is much better)
Survival
Mcgann
The TV Movie
Bolded episodes are REALLY BAD OK. I'm sorry, I'm so sorry, etc.