After watching the latest Doctor Who Christmas special, one thought kept sticking in our brains: When did the Doctor become so good at controlling his time machine, the TARDIS? He used to be unable to steer it at all.
The idea that the Doctor couldn't control his TARDIS was a huge part of the show's original concept. In the pilot, the Doctor kidnaps two schoolteachers from 1963 London and then decides to take them home after all — but for a year and a half, no matter what the Doctor does, he's unable to get Ian and Barbara back to their own time and place. (The closest he gets is when they arrive in the correct time and place, but only a few inches tall.)
Throughout the 1960s, companions poke fun at the Doctor's inability to land the TARDIS where, or when, he wants to, and it's a running joke that the machine has a mind of its own. (Something that it's since been hinted is more literally true.) And whenever the TARDIS lands somewhere at the start of an adventure, it generally stays there until the end, because if the Doctor tries to use it to get from point A to point B in the story, he'll probably wind up at point Z instead.
So when did this change?
After mulling this over for a bit, I'd have to say it started changing in the 1970s. First off, the Doctor gets trapped on Earth by the Time Lords, as a very dubious punishment for interfering in the affairs of lesser species. ("We'll punish you for meddling, by forcing you to live among the species you enjoy meddling with the most." It's sort of the Time Lord equivalent of torture via comfy chair.) After a year or so, though, the Doctor starts making trips in the TARDIS again, only the Time Lords are usually the ones sending him places where they need his delicate (ha) touch. The Time Lords, of course, have no trouble steering the TARDIS where they want it to go. And when they're done with him, the Doctor always bounces back to 1970s England.
But after the Time Lords release the Doctor from his exile, his control over the TARDIS seems to have improved marginally. For one thing, he can still always find his way back to late 20th century England, since half his supporting cast is waiting there. For another, he's able to follow Lynx the Sontaran back to the middle ages. And even though a big joke is made of the fact that the Doctor can't get the TARDIS to Metebelis 3 a few tries in a row, when Sarah Jane is in trouble there, he's suddenly able to steer the TARDIS to come to her aid just fine. In fact, he goes back and forth between Earth and Metebelis 3 a couple times in the final Jon Pertwee story, without winding up on ancient Raxacoricofallapatorius (as far as we know.)
Over the course of the Tom Baker era, the Doctor's control over his machine gets better and better. Sure, he boasts that he can take Sarah Jane from Scotland to London and arrive five minutes before they left — and totally fails to fulfill this promise. (But there are distress signals and Sutekh and confusing alien duplicates of England fouling him up.) On the plus side, though, he's able to steer the TARDIS to Scotland in the first place, in response to the Brigadier's telegraph requesting assistance.
(There's also the confusing thing where he sets the TARDIS controls for Antarctica, then flies a helicopter there, only to land the TARDIS in Antarctica on his next trip, when he's actually aiming for a beach planet.)
The following year, he's able to take the stone megalomaniac Eldrad back to the planet Kastria. He's able to travel back to his own homeworld, Gallifrey. He seems to land in Victorian London on purpose, since he and Leela both dressed for it. (Although his next trip hits Fang Rock instead of Brighton.) From then on, his control seems better and better. Even when the Doctor lands in the middle of an adventure at random, he's able to use the TARDIS to travel to someplace he needs to go, as necessary. (Like a medical asteroid, or the Fendahl homeworld.)
The Doctor's control over the TARDIS gets so good, in fact, that the show's writers seem to decide it's gone too far — so they introduce a random plot device. Literally.
At the end of "The Armageddon Factor," the Black Guardian — who's sort of a Space Devil with a bird on his head — swears eternal vengeance against the Doctor. The threat of the Black Guardian's vengeance is so terrible, the Doctor decides the only thing he can do is to install something called a Randomizer into the TARDIS — a device which makes the TARDIS land in random times and places. So the Doctor will never know where he's going, but neither will the vicious Black Guardian. Problem solved!
The Randomizer brings up all sorts of questions, which are never addressed. Like, wouldn't the TARDIS land in deep space almost every time? What's to stop the TARDIS materializing in the heart of a sun? Etc. etc. etc. Luckily, the writers pretty much ignore the Randomizer — until a year or so later, when the Doctor has to destroy it for some utterly random (sorry) reason.
Once the Randomizer's gone, it's pretty much the end of the Doctor's troubles with steering the TARDIS. He even remarks soon afterwards that "The TARDIS and I are getting rather better at these short hops." In this context, "short hop" means that he's piloting the TARDIS a mile or two, without traveling in time. That's a lot more precision than he'd been able to achieve even a few years earlier.
Soon enough, the Doctor is using the TARDIS to avoid walking a few miles, on a semi-regular basis. (I exaggerate slightly. But only slightly.) Just a year or so after the "short hops" comment, his companions Nyssa and Adric are even able to pilot the TARDIS a mile or so, from a forest to a country house, in "The Visitation." At the same time, the Doctor seems to be having trouble getting Tegan home to 1980-ish, causing her to scream at him. And the Doctor asks the TARDIS in exasparation why it keeps bringing him to 20th century Earth. (Just not the year Tegan wants.)
Pretty much throughout the 1980s, the Doctor seems to be able to get where he's going most of the time, even though the trope of the TARDIS having a mind of its own remains a potent one. A lot of the Doctor's steering ability seems to depend on quite how badly he wants to get somewhere, and what's at stake. (If you were cynical, you might argue that it really depends on whether the plot needs the Doctor to be able to steer the TARDIS or not.) The TARDIS is also increasingly vulnerable to collisions, time/space tunnels, and other assorted hazards that knock it off course.
And of course, the Sylvester McCoy version of the Doctor, with his constant scheming and habit of being ninety seven steps ahead of his enemies — plus his habit of taking his companion Ace to various locations and times where he wanted her to confront something traumatic — relied on the TARDIS being more or less controllable.
Then we jump forward to the new series, and apart from the occasional joke about the Doctor not having read the manual, I'm racking my brain to think of a time when he didn't have perfect control over the old girl. (Edited to add: as various people have pointed out in the comments, he has had some steering mishaps, especially in the Christopher Ecclestone era, like when he brings Rose home a year late. Post-Ecclestone, a lot of the steering mishaps seem to be of the "something interferes with the TARDIS or seizes control over it" variety, but not all. And the massive overshoot in "The Eleventh Hour" seems to be caused by a newly regenerated Doctor and TARDIS both having glitches.)
Of course, even though the Randomizer was a clunky plot device that pretty much never made sense, you can see why the writers wanted to introduce it — a Doctor whose destinations are totally random is more flawed and vulnerable, and thus possibly more fascinating. Plus with the Randomizer, he pretty much could never use the TARDIS to solve his problems.