There's a fair few I wouldn't mind seeing back, and a few additional things I'd like to add.
Some people have given the opinion that we shouldn't be seeing characters returning and that it's all about NEW companions and characters. But if we look at The End of Time and The Time of the Doctor, the former brought back Wilf and Donna whilst the latter 'brought back' Tasha Lem. Both of them featured a comeback, but the latter was a cop out because it was only a comeback from the characters perspective, not the viewers. We wasted the same amount of time getting familiar with Tasha Lem as we would have done getting familiar with, say, River Song. Except we're not given the novelty value, the sentiment or the sense of continuity. It happens a lot more recently - what with the still only vaguely covered introductions to the Paternoster Gang, and the complete lack of an introduction to characters in episodes like Dinosaurs on a Spaceship. For the record I much prefer The Time of the Doctor to The End of Time, but I think that there is something that can be said for a decent character return every now and again. This is a show revolving around time travel..forwards and back... the Doctor can always be moving forward but he doesn't have to completely disregard his past.
Anyway, onto the characters I would love to see make a comeback...
Jo Grant, last seen in SJA: Series 5, Death of the Doctor
One of only three companions from Classic Doctor Who to have been established in NuWho, along with Sarah-Jane Smith and The Brigadier. Most tragically we have lost Lis Sladen and Nick Courtney in recent years which leaves the wonderful Katy Manning. I thought she was absolutely wonderful in Death of the Doctor...a totally endearing asset to the story which was admittedly very cramped. She played alongside the Eleventh Doctor wonderfully, and I would absolutely love to see her again. Give her her own School Reunion -esque episode, perhaps set in an exotic filming location. Or, I'd love to see her join the TARDIS again for a handful of episodes like Captain Jack or Mickey did... it'd be interesting and different to see someone return to the life they'd left so long ago as a mini plot across a series...not full-time of course, but as a little something extra.
Craig Owens, last seen in DW: Series 6, Closing Time
I loved The Lodger and though I wasn't a fan of Closing Time it wasn't without merit. Craig was a very loveable character who was a great friend to the Eleventh Doctor. I'm not sure why but ever since it was announced he was making his first return to the show, I like many others envisioned a trilogy of sorts for him. We're still waiting on that Lodger3, but now seems the perfect time - Gareth Roberts is contributing to Series 8, we're going to want some familiar faces whilst the new Doctor establishes himself, and it would be totally different and quite hilarious to see Craig confront a Doctor with an all new Capaldi-face! Maybe give Craig a trip in the TARDIS once and for all... I think Colchester has been pretty exhausted of aliens.
Jack Harkness, last seen in TW: Miracle Day, Episode 10
I wanted to see him meet River Song at some point, and I think it'd still be rather funny seeing Barrowman and Kingston in the show together. He's the sort of character I could see coming back, and with Torchwood all but defunct now it might be a good way to get over that whole Miracle Day mess and give deserving fans some answers as to what ultimately became of his character. I'd not want Barrowman back in any unlikely fifth series of Torchwood anyway (much prefer to see a Victorian Torchwood...period drama sci-fi!) so I'd either bring him back when he's lived an awful lot longer (it'd explain Barrowman's ageing) or to explore those lost memories he mentioned back in Series 1. The character has been a bit useless in Doctor Who since the first series - he turns up with a few helpful guns now and then but he's not actually been really necessary. Capaldi is supposed to be a huge change in Doctor, and it'd be great to see Barrowman explore that. So long as we don't tarnish the fact that The Doctor happens to look a bit like John Frobisher, we're okay.
Donna Noble, last seen in DW: The Specials, The End of Time
I think they missed their best chance to bring her back in the 50th Anniversary, but I loved the character so much it feels odd to have not seen her make a comeback with her memories. I wouldn't want a full-on comeback, or one that rewrites the tragic conclusion to Journey's End, but to see her like she was through Series 4 would be a real treat. This one is probably the biggest fanboy-demand on my list and deep down I know it doesn't make much sense to see her back... but I can't help to ask for it.
River Song, last seen in DW: Series 7, The Time of the Doctor
Yes, her last appearance was a lovely and fitting potential goodbye, but such a timey-wimey character could still warrant a comeback. I don't care about Series 6 DVD boxset-extras, I want to see her and the Doctor at the Singing Towers. Again I think they missed the golden opportunity for this... a small, wordless cameo in The Time of the Doctor which saw The Doctor with his new haircut (conveniently supplied by Matt Smith) sitting on a hillside overlooking The Singing Towers. They both know he's about to change and that The Doctor must move on... what a cameo that would have been! Alas, we never got anything remotely like it and now never will, but if there was a convincing story for the character I'd love to see her back.
The Trickster, last seen in SJA: Series 3, The Wedding of Sarah-Jane Smith
An iconic villain from the spin-off, The Trickster has been worthy of a crucial passing mention in Doctor Who's Turn Left and Torchwood's Miracle Day. He appeared in stories from the first three series of SJA and was also meant to be the main antagonist in the never-filmed Series 5 finale The Battle of Bannerman Road. His mysterious 'Pantheon of Discord' was an ominous and forboding force, whilst his Brigade of aliens was menacing. He'd be a suitably dark villain in Doctor Who, having met The Doctor already in his Tenth incarnation. It would be a nice way to extend the legacy of Sarah-Jane as a character and a very decent spin-off show.
Tasha Lem, last seen in DW: The Anniversary Specials, The Time of the Doctor
It felt like a bit of a cheat to have a character The Doctor had met before that we hadn't, particularly in a regeneration story. The character was neither established as new, nor a familiar face. It distances The Doctor from the viewer as a character and makes you care less about the whole thing. Orla Brady is a brilliant actress and I wouldn't mind seeing her back in the role again if they were to explore it properly. The allusions to her being a bit too much like River Song were very interesting.
Madame Kovarian, last seen in DW: Series 6, The Wedding of River Song
The show lacks female villainy, and I'd really hoped that Kovarian would be the character to break the trend. She was a bit discarded come the end of Series 6, and come the brief wrap-up of her characters motives in The Time of the Doctor I feel that Moffat would hardly care to bring the character back. But she was mysterious, her fate remains unknown and she was played ever so wonderfully by Frances Barber. I rather liked the suggestion she could be The Rani...and why not bring the character back?! Make her a bit more of a credible threat than she used to be, give her motive and it would be a huge plot twist. I rather liked an idea thrown around on here by someone I can't recall that The Doctor, The Master, The Rani, Omega and a few others formed a group that went against Gallifrey and the Timelords. I think it'd be interesting to see how this group fell apart into adversaries, and it'd work to explain why they in particular were all outside of the Timelock. It'd allow for some interesting Timelord episodes without actually having to bring back Gallifrey anytime soon...that's a plot that should be played out over time.
Clara's Family, last seen in DW: The Anniversary Specials, The Time of the Doctor
Awkwardly shoehorned into Matt Smith's final story, I have truly missed the sense of family dynamic that earlier series had. I don't want it to become a domestic soap-fest of course, but family and housing estates help to give perspective to the alien planets we're seeing the rest of the time, establishing that sense of awe and wonder at the universe. Amy's family and Rory's Dad were only brought along when they were needed to serve the plot rather than the other way around... and it's a sad state of affairs that the likes of Wilf Mott and Jackie Tyler were as well-written as the actual companions we get now. I want that family vibe again, just don't overdo it.