I ran across a couple posts on WhatCulture arguing about what characters on other TV shows would make great companions and which ones would be terrible.
I don't think either list is very good, but the supposedly "Great Companion" list is by far worse. At the number one spot is Sheldon Cooper , whom I have already done a write-up (along with the rest of the BBT cast) over at the DWAITAS message board. Regardless of what that blog thinks, Sheldon would be terrible in the TARDIS. Considering that his entire self image (hell his whole reality!) is based around the idea that he is the smartest person in the room. Any time he's confronted by someone who could truly challenge him intellectually, he's either reverts to downright childish behavior (like when he's verbally sparred with Leslie Winkle) or completely shuts down, uncertain how to react (worst case being when Stephen Hawking pointed out a math error in his paper and he fainted.) The Doctor, in his usual show-offy manner, would have Sheldon turned into a puddle within minutes of meeting him, and the second a monster showed up, it would be a pretty good guess that Sheldon's Mother really would need to have him tested again.
Of the other choices on the "Great Companions" list, I'd say the kid from Touch, Chandler from Friends, and Hiro Nakamura from Heroes, are the equally bad for different reasons. Chandler is just an idiot, has nothing resembling useful skills, and unless the Daleks do us all a favor and exterminate him on sight he would be a total waste. The Kid and Hiro are pretty much on the opposite end of things, with too much power. Hiro's space-time bending and the kid's numerical clairvoyance would end up being power upgrades for deus ex machina that the Doctor often is.
As for the "Terrible Companions" list, I just think the writer just threw out some names and didn't really try. Personally, I think most of them would work not as Companions, but as potential antagonists and villains. Take Mr. Bean for example, what if he was some kind of temporal anomaly that acted as a kind of anti-Doctor. Popping up throughout history and wreaking havoc through his incompetent bumbling? Maybe he was chosen by the Black Guardian as his ultimate champion? What better instrument of Chaos and Disorder than someone who fully embodies such traits?
I could see situations where B.A. Baracus and the rest of the A-Team might find themselves in conflict with the TARDIS crew. It's not uncommon for Doctor Who stories to revolve around wealthy, powerful, and unscrupulous people. Henry Van Statten , Luke Rattigan, or Joshua Naismith are all the kind of men that will trample over as many backs needed to achieve their goals. This is exactly the kind of situation the A-Team would often be called in to rectify. Considering the standard operating procedure for the A-Team includes them storming their enemy's stronghold and delivering an ultimatum, it might be really bad timing they show up right as the bad guy starts up some big plot and things go awry due to their interference.
Wesley Crusher of course, was the child prodigy of Star Trek that ended up gaining some kind of Vortex manipulation powers from his friend the Traveler. And all of this happened (relatively speaking) before the Last Great Time War. It might be the Traveler's people found themselves involved in the Time War, and Wesley might have ended up on the front lines. Much like the Doctor, he ends up sacrificing much to save reality, maybe finding himself trapped in strange alternate universe where nothing of his future exists. The once bright and hopeful Starfleet officer is now a damaged war survivor with an agenda, to return home, whatever it takes. He's probably had to break a lot of the rules Starfleet and the Traveler instilled into him just to survive, and now he's willing to burn worlds just to go back to where he belongs.
They do list BBC's Sherlock on the "Terrible" list. Like some of the other characters, he would not be an outright villain, but someone who starts out on the opposite side of the TARDIS crew. If they are trying to keep a secret and Sherlock is hellbound determined to uncover it, that would provide quite a bit of conflict for an adventure without him actually being a straight off bad guy.
Now Ted Mosby from "How I Met Your Mother" is clearly an outright villain*. I suspect he's a memory changing entity like Adam Smith, and this intricate tale he's telling these kids is an attempt to make them believe he is their father and belongs in their lives.
Since I go by the belief that all of the Hitchhiker's books exist within the same reality as Doctor Who, I would assume the Doctor has run into Zaphod Beeblebrox on a few occasions. They would definitely be antagonistic in a long standing rivalry of one-upsmanship and juvenile pranksertism. I could definitely see their last drinking binge together ended with the Doctor waking up with a hell of a hangover and in the First Queen Elizabeth's bed.
It's unavoidable that everyone would have their own ideas for what character would be a great companion and which ones would be rubbish. The concept of the show lends itself so well to crossovers it's no surprise fans come up with ideas like this, and even less of a surprise fans comment incessantly about it:)
*And so is his actor, I mean, it's obvious the guy playing him is also some kind of experiment by the Silence to create a human with their abilities. Seriously, go look up his IMDB page and five minutes later, try remembering what his name is!