In The Chase, when the Doctor, Ian, Barbara and Vicki were captured by the Mechanoids (basically giant geodesic spheres with flamethrowers) (so, basically awesome), they found themselves imprisoned alongside Steven Taylor, a spaceship pilot from the 23rd century (or thereabouts). They believed Steven died during their escape, so Vicki and the Doctor were understandably surprised when, after saying goodbye to Ian and Barbara, they found Steven waiting for them in the TARDIS.
Steven had gone back into the city to rescue his stuffed panda HiFi, who had been his only companion during his two-year imprisonment (like Tom Hanks' volleyball, only more adorable). Steven survived the destruction of the Mechanoids' city and slipped into the TARDIS while nobody was paying attention. Here's Steven with Vicki and HiFi at the start of his next story, The Time Meddler:
Adorable, right? Enjoy the picture, it's the last interesting thing you'll see about Steven Taylor.
Steven was brought in to replace Ian as the leading man, the action hero (Barbara, of course, was irreplaceable). And he fits the bill fine - young, strapping, handsome, and utterly and completely generic. He's not a bad companion, he's fills a storytelling niche and Peter Purves does a good job with the material he's given. But after his exciting introduction, he doesn't do a whole lot; at least, nothing unexpected if you're familiar with his stock type. He gets very little in the way of character development - he's just kind of there.
Here's the new crew, hiding cheerfully behind a rock. Posing for publicity photos is fun!
Steven's development was not aided by the fact that his first few scripts were originally written for the previous TARDIS crew. In his next story, Galaxy 4, his role in the story and most of his dialogue were originally written for Barbara. As a consequence, he spends most of the story held hostage while the Doctor and Vicki get on with the business of saving the planet.
See? They even gave him one of Barbara's cardigans to wear.
He spent the next story, The Myth Makers, being all action heroey in the Trojan War, and getting near-mortally wounded for his trouble. Vicki departs in this story, and she's replaced by Trojan handmaiden Katarina, who carries the wounded Steven into the TARDIS.
More on Katarina next time, but suffice it to say, she doesn't last long. In the next story, The Daleks' Master Plan, she's quickly replaced with Sara Kingdom, who also doesn't last long. Steven was very, very lucky to have gotten out of that story alive.
All these deaths in the space of one story wear a bit on Steven, so the TARDIS takes him and the Doctor to Paris, where they can chillax in some fine BBC period clothing and get their drank on.
Except it's Paris in 1572, and the story is titled The Massacre of St Bartholomew's Eve, and ten thousand Huguenots, including all the drinking buddies Steven just made and the cute serving girl named Anne Chaplet he had his eye on, are all about to be brutally slain in a weeks-long purging that will see the streets of Paris run red with innocent blood. Because fuck you, Steven Taylor.
Every companion gets their lesson in the futility of changing history, and this was Steven's. He's furious at the Doctor for making them abandon their new-found friends to their fate, and when the TARDIS materializes in 1966 London, he storms out, determined to leave his travels with the Doctor behind forever. Ah, you say, that sounds like characterization to me! Well, no, because right away he spots some policemen running towards the TARDIS and comes back to warn the Doctor, who promptly takes off. On board the TARDIS with them this time is new companion Dodo Chaplet, and Steven convinces himself that, since they have the same last name, Dodo must be Anne's descendant, so Anne must have survived the massacre, and all is well. The Doctor is so happy Steven has stopped bitching about the constant slaughter that comes with a life in the TARDIS that he doesn't point out how staggeringly unlikely Steven's hypothesis is.
Here's the new team in Dodo's first full story, The Ark. Steven doesn't do much in this one, except almost die from catching Dodo's cold. It's a nice picture, though, isn't it?
Steven gets to have a bit more fun when the crew goes up against The Celestial Toymaker. The Doctor is sidelined for most of the story (the producers were considering letting William Hartnell go, as he was becoming more and more difficult to work with), so Steven and Dodo took the lead, playing the Toymaker's deadly games in order to win back the TARDIS.
Sadly, most of this story is lost, but it sounds like it was pretty good. Steven got lots of action in this one, and doesn't he look nice in color? Score one for you, Steven Taylor.
I take it back. In The Gunfighters, the trio visit Tombstone just in time for the gunfight at the OK Corral. They meet the Earps, the Clantons, Doc Holliday and Johnny Ringo, bullets fly and people die, and Steven dresses like he's going to a Western-themed costume party at Liberace's house. Luckily, the Doctor passes them all off as entertainers, and even more luckily - and inexplicably - Steven can sing and play the piano. There's an awful lot of gunfighting in this story, and Steven doesn't take part in any of it. Ian would have taken out the entire Clanton gang with one bullet...sigh. I miss Ian.
But all mediocre things must come to an end, and Steven's next story, The Savages, was his last. On an unnamed future world, the Doctor negotiates peace between a race of scientific Elders and the primitive Savages they've been exploiting. For some reason the two tribes invite Steven to stay with them and become their leader - I suppose when choosing a leader after years of conflict, "vaguely nonthreatening" seems like a pretty attractive quality. Steven accepts, bidding the Doctor and Dodo farewell.
I've probably been overly harsh on Steven - he was perfectly serviceable, as male companions go. He was just bland, and it's hard to find anything funny or interesting too say about bland people.
Oh, I've got something. In the tie-in novel The Empire of Glass, set in 1609 Venice, Steven teams up with playwright Christopher Marlowe, who makes a pass at him. Steven ignores it, though, because otherwise something interesting might happen.