5) Rita, "The God Complex"
As far as we know, the Doctor doesn't usually travel with openly religious people: he did take along a Greek handmaiden who thought that the TARDIS was the afterlife back in the day, but let's just say that didn't work out so well. It would have been refreshing to pair him with Rita, a practical, three-dimensional Muslim med student, who had to reconcile her devout beliefs with her deep fear of failure, as embodied by her father. Everything about Amara Karan's performance would have screamed "new companion" in other circumstances. Even the Doctor was taken with her pretty much immediately, another sign she wasn't going to make it. So guess what? She didn't, courtesy of a hungry space minotaur.
4) Brian Williams
Not the news anchor, although I think he'd be an amazing companion as well, but Rory's father, played by the former Arthur Weasely, Mark Williams. I think most of us can admit that Brian was introduced way too late in the game: his shift from grouchiness to wide-eyed wonder was one of the few spots of genuine emotion in the often frenetic and artificial-feeling Series 7. He could have been a great temporary companion a la Mickey, barging on board the TARDIS every once and while and making embarrassing remarks about his golf balls. He also clearly wants to see the universe, so much so that the Doctor invites him and he actually turns it down to take care of the plants. Apparently no one told him that a time machine could just take you right back to when you'd left, although knowing the Doctor's track record, that's probably not the best thing to count on. All of us wondering what happened to the apparently only family member left in the lurch by Rory and Amy's departure did get a little bit of closure through the reconstructed "deleted scene."
3) Jackson Lake, "The Next Doctor"
I mean, the guy didn't get to be the Doctor, so you'd think making him the companion would have been the least RTD could have done. But no. Twas not to be. David Morrissey gave a spirited performance and outshone the material as a man who was almost a Doctor (but definitely not "The Next," a point that still irks me to this day). I don't know if Morrissey was ever actually considered to be the title role, but it certainly wouldn't have bothered me if he somehow came back as number 12 in the greatest continuity boomerang arc ever. As the episode began winding down, some of us Blackpool fans might have got a giddy thrill at Lake's suggestion that he and Tennant go for "one more adventure." But, in one of the lamest cop-outs in the show's history, the mere fact of stepping inside the TARDIS proves too much for Lake and he decides that's enough. Pathetic.
I guess it's probably for the best that this was just a one-off, as Jackson probably would have wet himself and exploded if he saw an iPad. Actually, it doesn't really make any sense: you can handle flying over London to battle a giant Cyberman but a big room is too much for you? As you may know, Morrissey found stable employment anyway on a little AMC show you've probably never heard of, but let's give a big "le sigh" for what might have been.
2) Kate (Lethbridge) Stewart
Granted, although I haven't heard any rumors yet, I'd be surprised if we didn't see more of Jemma Redgrave sometime soon. The daughter of old series mainstay Alistair Gordon Lethbridge Stewart (a.k.a. The Brigadier/The Brig/Brigadoon/B-unit etc.), Kate (who prefers the last name "Stewart") has so far only appeared in one canonical episode, last half-series' "The Power of Three." Before that, she was portrayed by Beverly Cressman in some Doctor-less direct-to-video spinoffs written by Marc Platt. I wish she had been introduced sooner in the revived series, as she's a great idea for a character and there's so much to explore there. However, it would be nice if the daughter of the Brig, a man known for being earthbound and sensible, got to spend regular time among the stars with her dad's old sparring partner. And she could bring a little bit of old-school mythos and depth to the Doctor's travels as we find out what being part of the UNIT family does to you. But right now, I just hope we see her again at all, and that next time she isn't flummoxed by a bunch of cubes.
1) Wilfred Mott
Bernard Cribbins is a treasure, and the character of Wilfred Mott, Donna Noble's lovable grandfather, was a welcome addition to the Who character stable, and helped distinguish Donna's family from the supporting characters before her. Technically, yes, Wilfred was a companion for the Tenth Doctor's last two episodes and was billed as such, but you know what I mean. I wanted a good chunk, and maybe even the entirety of a season with the crazy old man in tow. From his first appearance as a souvenir vendor in "Voyage of the Damned," you knew there was something about this guy, and I'm happy we got to spend more time with him. But there should have been even more. Under his happy-go-lucky exterior was a melancholy past, and his heart-to-hearts with Tennant's Doctor are some of the most moving of his run, and maybe the entire series. And yes, we now all know the role that Mott played in the Doctor's life and why the two of them were linked, but for a little bit there was the suggestion of something more, particularly in his link to the lady in white, known officially as The Woman. Who this woman was is the Doctor's equivalent of Lost's Mother, something we'll probably never really know (and come to think of it, The Woman was hinted at as being the Doctor's mother. Hmmm...).
Anyways, Wilf was great, and proved himself as skillful in combat as he was soulful in contemplation. But we'll always have his appearance from the Who-themed episode of Never Mind the Buzzcocks, in which he sang his novelty tune from the sixties and was almost drafted to write for The Mighty Boosh. And this man could have traveled through time with us. Oh well. Such is the whim of the timestream. We can take consolation that he may have traveled with the Doctor before in another, snazzier life. I wonder if that sort of overlap makes the Doctor's nose twitch.