Unlike most companions, but for obvious reasons, there is a fair amount of spinoff media about Susan's life before her first TV appearance. I particularly recommend the Telos novellas Frayed by 'Tara Samms' (a pseudonym for Stephen Cole) and Time and Relative by Kim Newman, which explore respectively the Doctor and Susan's choice of names and what happened in London in the winter of 1962. There are also a bunch of short stories in the various Short Trips anthologies set in the pre-Ian and Susan period.
Susan appears in The Five Doctors as one of the main characters, but we hear nothing about what she has been up to since leaving the Tardis. The Eighth Doctor novel Legacy of the Daleks by John Peel has her helping the doctor defeat the Delgado!Master. The Eighth Doctor audio An Earthly Child has her and her son (who is played by Paul McGann's son) thwarting an alien invasion. The BBC audio Whatever Happened to Susan Foreman? has her becoming European Commissioner for Education in the mid-1990s. There are also two Big Finish stories featuring an alternate Susan with Geoffrey Bayldon as the Doctor; she becomes President of the Time Lords. Take your pick. (She is also in Dimensions in Time, but we don't talk about that.)
Ian and Barbara
It is pretty much received wisdom that Ian and Barbara got married after leaving the Tardis ans returning to 1965. In David McIntee's novel The Face of the Enemy they are roped in by UNIT to join the Delgado!Master in dealing with curious events relating to many televised adventures. their son, rock singer Johnny Chess full name John Alydon ganatus Chesterton) turns up in Keith Topping's novel The King of Terror and has a fling with Tegan. We heard in Death of the Doctor (SJA) that they had both become professors at Cambridge and had not aged since the 1960s.
In a brilliant short story, "Apocrypha Bipedium" (Short Trips: Companions), Vicki/Cressida meets up with the Eighth Doctor, Charley Pollard and a young William Shakespeare in the immediate aftermath of the rather duff Eight/Charley audio The Time of the Daleks. The Big Finish audio Frostfire by Marc Platt has quite a substantial framing narrative set in Carthage many years after The Myth Makers, though most of the plot involves Jane Austen in 1814.
Apparently Steve Lyons' short story, "Katarina in the Underworld" (Short Trips: The Muses) describes her afterlife following her death in The Daleks' Master Plan, but I haven't read it. Lyons is a good writer though so I shall look out for it.
Big Finish have done three Companion Chronicles featuring Jean Marsh as Sara Kingdom, with an imaginative solution to how you can write stories about a dead character: Home Truths, The Drowned World and The Guardian of the Solar System, all by Simon Guerrier, all recommended.
Uniquely, nobody seems to have written anything about what happened to Steven on the planet of the Elders and the Savages, despite Peter Purves' repeated and increasingly plaintive statements that he would love to reprise the role in such a story. (Maybe he should write it himself - see below under Mike Yates and Harry Sullivan.) I'm really rather surprised by this: how can it possibly have come about that there are more post-Tardis stories about Kamelion than about Steven??? [Edited to add: Apparently this is due to problems with the estate of Ian Stuart Black, who retain copyright in the planet of the Elders and Savages.]
Having had one of the worst write-outs of any companion, Dodo gets one of the better afterstories in David Bishop's novel Who Killed Kennedy?, in which the narrator, James Stevens, discovers her after years of treatment for psychiatric problems, and has a love affair with her which ends tragically. Though in "Ships" by Jamie Woolley, published in DWM 185 in 1992, she is still alive.
Ben and Polly
There are a couple of short stories about Ben and Polly finally getting together (unlike Ian and Barbara, their love is not generally assumed to be plain sailing) and in Death of the Doctor (SJA) we are told that they are running an orphanage in India. However...
Polly without Ben
In Marc Platt's typically intricate Big Finish audio The Three Companions, Polly joins forces with the Brigadier and audi-only companion Thomas Brewster to thwart alien forces casuing climate change. We are told that she is now working in a senior position in Whitehall, so presumably Ben has found someone else of the same name to run his orphanage with.
Victoria foolishly returned to Det-Sen monastery in the early 1990s and became possessed by the Great Intelligence; under its direction she ended up running a sinister north London university and had to be rescued by the Brigadier and Sarah Jane Smith, as shown in yet another Marc Platt story, Downtime. In The Great Space Elevator, she is expecting her first grandchild (presumably in 2008). (She is also in Dimensions in Time, but we don't talk about that.)
Zoe appears as an illusory flashback in The Five Doctors, and has a post-Tardis framing narrative in the audio Fear of the Daleks; and Big Finish found an imaginative way of bringing her back in Legend of the Cybermen. But I particularly want to flag up Peter Anghelides' short story "The Tip of the Mind" in the Short Trips: Companions anthology, which features a rather moving encounter between an amnesiac Zoe and the Third Doctor.
Jamie also appears as illusion in The Five Doctors; but it seems that after the Second Doctor's trial, the Time Lords sent the two of them on a couple of special missions - as in The Two Doctors and Terrance Dicks' novel World Game. The recent Big Finish audio sequence comprising City of Spires, Night's Black Agents, The Wreck of the Titan and Legend of the Cybermen brings back an older Jamie for adventures with the Sixth Doctor (and in the last of these also Zoe). DWM got there years before, though, actually killing Jamie off in a Six/Peri comic story, "The World Shapers", published in 1987 in ssues 127-129. [Edited to add: see also the framing narrative of Big Finish audio The Glorious Revolution.]
Her actual departure isn't shown on TV, but it is covered in Gary Russell's novel The Scales of Injustice. Liz also appears briefly in Who Killed Kennedy? and as an illusion in The Five Doctors, and apparently features in several novels I haven't read - Blood Heat, The Devil Goblins from Neptune, The Wages of Sin and Eternity Weeps in which she is killed off. The four P.R.O.B.E. videos feature her as the leader of the Pretenatural Research Bureau, with Louise Jameson playing her sidekick and numerous other Who actors involved (in particular the first features Jon Pertwee, Colin Baker, Silvester McCoy, and the third Peter Davison), but only Caroline John is explicitly playing the same role as on Who. [Edited to add: According to Death of the Doctor she is on the Moon.] (She is also in Dimensions in Time, but we don't talk about that.)
Her reappearance in last month's Death of the Doctor (SJA) was what prompted me to write this entry. She had previously sent the Metebelis crystal back in Planet of the Spiders; opinion varies on whether she split up with Cliff Jones (Paul Leonard's novel Genocide) or stayed with him (Death of the Doctor, Big Finish audio The Doll of Death). She also had a very weird experience doing her Christmas shopping in late 2010 (Big Finish audio Find and Replace). It is reported in 2040 that she died in a house fire in 2028 ("Carpenter/Butterfly/Baronet" by Gareth Wigmore in Short Trips: 2040).
The first TV companion to get a comeback after his departure, if you count Planet of the Spiders; and he is one of the illusory companions in The Five Doctors. Also features in Paul Cornell's Seventh Doctor novels No Future and Happy Endings, and is also the central character of the Doctor-less novel The Killing Stone by none other than Richard Franklin, which brings him together with the Brigadier and Benton to confront the Master (published as an audiobook by BBV in 2002). Most recently, of course, he has teamed up with the Fourth Doctor for two series of audio adventures. (He is also in Dimensions in Time, but we don't talk about that.)
Crumbs, where to start? Apart from the TV stories Mawdryn Undead, The Five Doctors, Battlefield and Enemy of the Bane (SJA); Marc Platt's Downtime; Big Finish audios The Spectre of Lanyon Moor, Minuet in Hell, Zagreus and The Three Companions; the Big Finish UNIT series; the Big Finish stories with David Warner as the Doctor; various novels including No Future and Happy Endings; and the 2007 Tenth Doctor comic story The Warkeeper;s Crown; apart from those few exceptions, we have no idea what happened to him after Terror of the Zygons. [Edited to add: According to Death of the Doctor he is in Peru. Again.] (He is also in Dimensions in Time, but we don't talk about that.)
Benton is the central character of Wartime, which was the first serious spinoff Who video; I haven't seen it (though reports are not terribly encouraging). Other post-Android Invasion appearances include the novel No Future and cameos in the novel Happy Endings and John Peel's novelisation of The Power of the Daleks. The Brigadier reports that he is now a used car salesman in Mawdryn Undead.
Harry actually gets prequelled in The Face of the Enemy; and Ian Marter wrote a spinoff novel about him, Harry Sullivan's War, which was published by Target back in the 1990s (Marter also wrote novelisations of two of Harry's TV stories, Ark in Space and The Sontaran Experiment). Apparently he is in Justin Richards' novels Millennium Shock and System Shock which are both reasonably high on my to-read pile. He is reported to have died in both Jacqueline Rayner's novel Wolfsbane, and The Wedding of Sarah Jane Smith (SJA), though in Russell T. Davies' novel Damaged Goods, set in 2015, he is still alive. Sarah says in Death of the Doctor (SJA) that he saved thousands of lives by vaccinating people. His brother Will features in the second run of audio sarah Jane Smith stories.
Sarah Jane Smith
Now in her fourth series of spinoff TV show, which follows two Big Finish series of audio plays about her and her appearances in K9 and Company: A Girl's Best Friend, The Five Doctors (and Downtime) and her New Who appearances in School Reunion. (and The Stolen Earth / Journey's End and The End of Time II). Also appears in Lawrence Miles' two-part Interference novel, and appears to be killed off in David McIntee's Bullet Time though is clearly alive and well some time later in other stories. (She is also in Dimensions in Time, but we don't talk about that.)
We see her life on Gallifrey with Andred and K9 Mark 1 in the novel Lungbarrow and the audio story Zagreus, and she then joins forces with Romana for Big Finish's three excellent series of Gallifrey audios; apparently a fourth is on its way. In three Companion Chronicle audios - The Catalyst, Empathy Games and The Time Vampire - she appears to be imprisoned and dying, but we don't really find the sequence of events leading up to this. (She is also in Dimensions in Time, but we don't talk about that.)
Romana ends up returning to Gallifrey (Big Finish audio The Chaos Pool) and becomes President (Paul Cornell's novels Goth Opera and Happy Endings; the Eighth Doctor version of Shada; Big Finish audios The Apocalypse Element, Neverland and Zagreus), eventually teaming up with Leela to try and save Gallifrey in the excellent Big Finish Gallifrey series (which at one point also brings back Mary Tamm as a development of Romana's first incarnation). A regenerated third version of Romana appears in the novels The Shadows of Avalon and The Ancestor Cell. (She is also in Dimensions in Time, but we don't talk about that.)
Mark I: Having stayed on Gallifrey with Leela, is destroyed during the finale of the second series of Gallifrey audios, but somehow gets transferred and regenerated to future London for the K9 spinoff TV series.
Mark II: Returns to Gallifrey with Romana and has quite a sparky relationship with Mark I before the other one gets destroyed. Fate after the Great Time War is unknown.
Mark III: May possibly be the K9 who travels with the Fourth Doctor and Adric in the stories of the 1982 Doctor Who Annual, before being sent off to join Sarah Jane Smith. Broke down irretrievably in "Moving On" by Peter Anghelides (Decalog 3: Consequences) and dismantled by Hilda Winters in the first Sarah Jane Smith audio series, before being repaired by the Doctor in School Reunion.
Mark IV: shouldn't really be on this list as has never travelled with the Doctor; but continues to appear occasionally on SJA and New Who. In David Martin's 1986 Make Your Own Adventure novel, Search for the Doctor, set in the year 2056, he is bequeathed to an unnamed viewpoint character [thanks for correction].
(Other/Unknown: There is also a K9 in Dimensions in Time, but we don't talk about that.)
Adric was rather boldly brought back from the dead by Big Finish in The Boy That Time Forgot, this time played by Andrew Sachs (or as Peter Davison puts it, "this time played by an actor"). It turns out that he survived the freighter crash and now rules over a race of intelligent scorpions, which works better than it sounds.
Peter Darvill-Evans' novel Asylum has Nyssa meeting the Fourth Doctor after she has left the Tardis but much earlier in the Doctor's timeline. Two of the four stories in the Big Finish audio Circular Time are vignettes of her life after the Tardis, and fifty years after Terminus she rejoins the Fifth Doctor, Tegan and Turlough in Big Finish audios Cobwebs, The Whispering Forest and The Cradle of the Snake, with more to come. (She is also in Dimensions in Time, but we don't talk about that.)
Apart from the possibly non-canonical incident where she teams up with the Sixth Doctor (In A Fix With Sontarans), we next find Tegan in Brisbane in 2006, briefly reunited with the Fifth Doctor but apparently suffering from a terminal illness, in the Big Finish audio The Gathering. However she seems to have recovered; according to Sarah Jane in Death of the Doctor (SJA) she is fighting for Aboriginal rights.
Turlough appears with the Sixth Doctor and Peri in Michael Holt's 1986 Make Your Own Adventure novel Crisis in Space. He also has an entire spinoff novel about his subsequent career, Turlough and the Earthlink Dilemma by Tony Attwood, which is really for completists only.
To my astonishment, there are several stories featuring Kamelion post-Planet of Fire. In Christopher Bulis' novel The Ultimate Treasure he is resurrected and destroyed again; in Matthew Griffiths' short story "The Reproductive Cycle" (Short Trips: Life Science) it is revealed that he somehow had a child with the Tardis; and he makes an appearance also in the last part of the Circular Time audio.
I have to say that in my personal fanon poor Peri is mindwiped and killed during the events of Mindwarp, and the subsequent assurances that she survived are false. However, I'm in a minority. In Age of Chaos, a full-length comic story by Colin Baker himself, the Sicth Doctor goes to Thoros Alpha to find her; David Carroll's 1992 short story "Reunion" in DWM 191 has her still annoyed with the Doctor; and in Matthew Jones' novel Bad Therapy the Seventh Doctor returns her to Earth. (She is also in Dimensions in Time, but we don't talk about that.)
Mel reappears in Steve Lyons' novel Head Games, and her subsequent travels feature in two short stories in the More Short Trips anthology, Gary Russell's "Missing, Part One: Business as Usual" and Robert Perry and Mike Tucker's "Missing, Part Two: Message in a Bottle". She is reported to have died in Dale Smith's novel Heritage. The Big Finish Unbound audio He Jests At Scars... explores what might have happened if the Valeyard had won. (She is also in Dimensions in Time, but we don't talk about that.)
Last but by no means least (indeed featuring in more spinoff literature than any other TV companion), because the TV series ended with her still in the Tardis, Ace features in 34 novels of the New Adventures series, all of which are presumably set after Survival, in 22 main sequence Big Finish audios (as well as others set before Survival), and in 18 DWM comic stories. Her ultimate fate is not clear: according to Sarah Jane Smith in Death of the Doctor (SJA) a "Dorothy something" is running a company called A Charitable Earth (initials suggesting that this is Ace rather than Dodo Chaplet); she is apparently killed in "Ground Zero", a DWM comic story by Scott Gray published in issues 238-242 in 1996; and most radically of all, in the webcast Death Comes To Time she actually becomes a Time Lord herself. (She too is in Dimensions in Time, but we really really really don't talk about that.)
This piece is much longer than I expected anyway but once I got started it just grew! Please do comment if I have made any particularly egregious omission. I had originally meant to link to my reviews of books mentioned above, and may still do that, but writing this has taken me all day and I want to finish up now. I think this all illustrates the wisdom of Paul Cornell's essay on canonicity from a couple of years back. Much briefer thoughts on the subject are embedded in a typically long and witty review of Death of the Doctor by an unspecified Daddy (probably Richard) on Millennium Elephant's blog.