Doctor Who suggested viewing order (revised).
Some introductory notes:
1. Doctor Who as a television show ran from 1963 to 1989, with a follow-up feature film released in 1996. Some people like to watch some or all of the earlier material before beginning with the "rebooted" show that began in 2005. This list is focused only on the modern, rebooted version of the show, although if you are interested in my recommendations for which pre-2005 stories to watch first, you can find that list here.
2. Doctor Who is often billed as a show for the whole family, whereas Torchwood is explicitly aimed at more mature audiences and The Sarah Jane Adventures is geared towards children. Though they share a common continuity, and although events and characters occasionally cross over between shows, they are tonally quite distinct.
3. This list includes all full episodes in the New Whoniverse, as well as certain supplementary materials such as mini-episodes that I feel represent a meaningful addition to the canon. Quotation marks appear around the titles of the latter, to distinguish them from full episodes on this list.
4. There are other non-episode features that I do not consider of central importance that have been omitted from this list.
5. When possible, I have grouped episodes of the same show in blocks together, to limit the sometimes jarring transitions that can arise when switching from one program to another. However, I have also tried to space the shows out so that their seasons are still running roughly parallel with one another. Hopefully, a good balance has been struck in that regard, and an effort has been made to not switch between the shows during major story arcs.
6. The show The Sarah Jane Adventures ties in with the main show's continuity less frequently than Torchwood does. As such, those episodes have been placed mostly where they seem to fit thematically, in addition to necessary plot reasons.
7. The Sarah Jane Adventures ended in 2011, after the death of its lead actress, Elisabeth Sladen. Torchwood aired its most recent episode in 2011 as well, but it or some other spin-off may yet air future episodes.
My suggestion of the order to watch episodes of Doctor Who, Torchwood, and The Sarah Jane Adventures:
Doctor Who 1.1 - Rose
Doctor Who 1.2 - The End of the World
Doctor Who 1.3 - The Unquiet Dead
Doctor Who 1.4 - Aliens of London
Doctor Who 1.5 - World War Three
Doctor Who 1.6 - Dalek
Doctor Who 1.7 - The Long Game
Doctor Who 1.8 - Father's Day
Doctor Who 1.9 - The Empty Child
Doctor Who 1.10 - The Doctor Dances
Doctor Who 1.11 - Boom Town
Doctor Who 1.12 - Bad Wolf
Doctor Who 1.13 - The Parting of the Ways
Doctor Who "Children in Need 2005"
Doctor Who 2.X - The Christmas Invasion
Doctor Who 2.1 - New Earth
Doctor Who 2.2 - Tooth and Claw
Doctor Who 2.3 - School Reunion
Doctor Who 2.4 - The Girl in the Fireplace
Doctor Who 2.5 - Rise of the Cybermen
Doctor Who 2.6 - The Age of Steel
Doctor Who 2.7 - The Idiot's Lantern
Doctor Who 2.8 - The Impossible Planet
Doctor Who 2.9 - The Satan Pit
Doctor Who 2.10 - Love & Monsters
Doctor Who 2.11 - Fear Her
Doctor Who 2.12 - Army of Ghosts
Doctor Who 2.13 - Doomsday
Doctor Who 3.X - The Runaway Bride
Doctor Who 3.1 - Smith and Jones
Doctor Who 3.2 - The Shakespeare Code
Torchwood 1.1 - Everything Changes
Torchwood 1.2 - Day One
Torchwood 1.3 - The Ghost Machine
Torchwood 1.4 - Cyberwoman
Doctor Who 3.3 - Gridlock
Doctor Who 3.4 - Daleks in Manhattan
Doctor Who 3.5 - Evolution of the Daleks
Torchwood 1.5 - Small Worlds
Torchwood 1.6 - Countrycide
Torchwood 1.7 - Greeks Bearing Gifts
Torchwood 1.8 - They Keep Killing Suzie
Torchwood 1.9 - Random Shoes
Doctor Who 3.6 - The Lazarus Experiment
Doctor Who 3.7 - 42
Doctor Who 3.8 - Human Nature
Doctor Who 3.9 - The Family of Blood
Doctor Who 3.10 - Blink
The Sarah Jane Adventures 1.X - Invasion of the Bane
Torchwood 1.10 - Out of Time
Torchwood 1.11 - Combat
Torchwood 1.12 - Captain Jack Harkness
Torchwood 1.13 - End of Days
Doctor Who 3.11 - Utopia
Doctor Who 3.12 - The Sound of Drums
Doctor Who 3.13 - Last of the Time Lords
Doctor Who "Time Crash"
Doctor Who 4.X - Voyage of the Damned
The Sarah Jane Adventures 1.1/1.2 - Revenge of the Slitheen
The Sarah Jane Adventures 1.3/1.4 - Eye of the Gorgon
The Sarah Jane Adventures 1.5/1.6 - Warriors of Kudlak
Torchwood 2.1 - Kiss Kiss, Bang Bang
Torchwood 2.2 - Sleeper
Torchwood 2.3 - To the Last Man
Doctor Who 4.1 - Partners in Crime
Doctor Who 4.2 - The Fires of Pompeii
Doctor Who 4.3 - Planet of the Ood
Torchwood 2.4 - Meat
Torchwood 2.5 - Adam
Torchwood 2.6 - Reset
Torchwood 2.7 - Dead Man Walking
Torchwood 2.8 - A Day in the Death
Doctor Who 4.4 - The Sontaran Stratagem
Doctor Who 4.5 - The Poison Sky
Doctor Who 4.6 - The Doctor's Daughter
Torchwood 2.9 - Something Borrowed
Torchwood 2.10 - From Out of the Rain
Torchwood 2.11 - Adrift
Doctor Who 4.7 - The Unicorn and the Wasp
Doctor Who 4.8 - Silence in the Library
Doctor Who 4.9 - Forest of the Dead
Doctor Who 4.10 - Midnight
The Sarah Jane Adventures 1.7/1.8 - Whatever Happened to Sarah Jane?
The Sarah Jane Adventures 1.9/1.10 - The Lost Boy
Torchwood 2.12 - Fragments
Torchwood 2.13 - Exit Wounds
Doctor Who 4.11 - Turn Left
Doctor Who 4.12 - The Stolen Earth
Doctor Who 4.13 - Journey's End
The Sarah Jane Adventures 2.1/2.2 - The Last Sontaran
The Sarah Jane Adventures 2.3/2.4 - The Day of the Clown
The Sarah Jane Adventures 2.5/2.6 - Secrets of the Stars
The Sarah Jane Adventures 2.7/2.8 - The Mark of the Berserker
The Sarah Jane Adventures 2.9/2.10 - The Temptation of Sarah Jane Smith
The Sarah Jane Adventures 2.11/2.12 - Enemy of the Bane
Torchwood: Children of Earth 3.1 - Day 1
Torchwood: Children of Earth 3.2 - Day 2
Torchwood: Children of Earth 3.3 - Day 3
Torchwood: Children of Earth 3.4 - Day 4
Torchwood: Children of Earth 3.5 - Day 5
Doctor Who The Next Doctor
The Sarah Jane Adventures 3.1/3.2 - Prisoner of the Judoon
The Sarah Jane Adventures 3.3/3.4 - The Mad Woman in the Attic
Doctor Who Planet of the Dead
The Sarah Jane Adventures 3.5/3.6 - The Wedding of Sarah Jane Smith
The Sarah Jane Adventures 3.7/3.8 - The Eternity Trap
Doctor Who The Waters of Mars
Doctor Who "Dreamland"
The Sarah Jane Adventures 3.9/3.10 - Mona Lisa's Revenge
The Sarah Jane Adventures 3.11/3.12 - The Gift
Doctor Who The End of Time Part I
Doctor Who The End of Time Part II
Doctor Who 5.1 - The Eleventh Hour
Doctor Who "Meanwhile in the TARDIS Part I"
Doctor Who 5.2 - The Beast Below
Doctor Who 5.3 - Victory of the Daleks
Doctor Who 5.4 - The Time of Angels
Doctor Who 5.5 - Flesh and Stone
The Sarah Jane Adventures 4.1/4.2 - The Nightmare Man
The Sarah Jane Adventures 4.3/4.4 - The Vault of Secrets
Doctor Who "Meanwhile in the TARDIS Part II"
Doctor Who 5.6 - The Vampires of Venice
Doctor Who 5.7 - Amy's Choice
Doctor Who 5.8 - The Hungry Earth
Doctor Who 5.9 - Cold Blood
Doctor Who 5.10 - Vincent and the Doctor
Doctor Who 5.11 - The Lodger
Doctor Who 5.12 - The Pandorica Opens
Doctor Who 5.13 - The Big Bang
The Sarah Jane Adventures 4.5/4.6 - Death of the Doctor
The Sarah Jane Adventures 4.7/4.8 - The Empty Planet
Doctor Who 6.X - A Christmas Carol
Doctor Who "Space"
Doctor Who "Time"
Doctor Who "Night and the Doctor - Good Night"
The Sarah Jane Adventures 4.9/4.10 - Lost in Time
The Sarah Jane Adventures 4.11/4.12 - Goodbye, Sarah Jane Smith
Doctor Who 6.1 - The Impossible Astronaut
Doctor Who 6.2 - Day of the Moon
Torchwood: Miracle Day 4.1 - The New World
Torchwood: Miracle Day 4.2 - Rendition
Torchwood: Miracle Day 4.3 - Dead of Night
Doctor Who 6.3 - The Curse of the Black Spot
Doctor Who 6.4 - The Doctor's Wife
Torchwood: Miracle Day 4.4 - Escape to L.A.
Torchwood: Miracle Day 4.5 - The Categories of Life
Torchwood: Miracle Day 4.6 - The Middle Men
Doctor Who 6.5 - The Rebel Flesh
Doctor Who 6.6 - The Almost People
Doctor Who 6.7 - A Good Man Goes to War
Doctor Who "The Battle of Demons Run: Two Days Later"
Torchwood: Miracle Day 4.7 - Immortal Sins
Torchwood: Miracle Day 4.8 - End of the Road
Doctor Who "Let's Kill Hitler: Prequel"
Doctor Who 6.8 - Let's Kill Hitler
Doctor Who 6.9 - Night Terrors
Doctor Who 6.10 - The Girl Who Waited
Doctor Who 6.11 - The God Complex
Torchwood: Miracle Day 4.9 - The Gathering
Torchwood: Miracle Day 4.10 - The Blood Line
Doctor Who 6.12 - Closing Time
Doctor Who 6.13 - The Wedding of River Song
The Sarah Jane Adventures 5.1/5.2 - Sky
The Sarah Jane Adventures 5.3/5.4 - The Curse of Clyde Langer
The Sarah Jane Adventures 5.5/5.6 - The Man Who Never Was
Doctor Who "Night and the Doctor - First Night"
Doctor Who "Night and the Doctor - Last Night"
Doctor Who 7.X - The Doctor, the Widow and the Wardrobe
Doctor Who "Pond Life Part One - April"
Doctor Who "Pond Life Part Two - May"
Doctor Who "Pond Life Part Three - June"
Doctor Who "Pond Life Part Four - July"
Doctor Who "Pond Life Part Five - August"
Doctor Who 7.1 Asylum of the Daleks
Doctor Who 7.2 Dinosaurs on a Spaceship
Doctor Who 7.3 A Town Called Mercy
Doctor Who 7.4 The Power of Three
Doctor Who 7.5 The Angels Take Manhattan
Doctor Who "The Great Detective"
Doctor Who "Vastra Investigates: A Christmas Prequel"
Doctor Who The Snowmen
Doctor Who 7.6 The Bells of Saint John
Doctor Who 7.7 The Rings of Akhaten
Doctor Who 7.8 Cold War
Doctor Who 7.9 Hide
Doctor Who 7.10 Journey to the Centre of the TARDIS
Doctor Who 7.11 The Crimson Horror
Doctor Who 7.12 Nightmare in Silver
Doctor Who 7.13 The Name of the Doctor
Doctor Who "The Night of the Doctor"
Doctor Who The Day of the Doctor