As a long time Dr Who fan (like nearly 30 years long time) this is a more challenging task than you might think.
I’ve had to try and sell Dr Who to a succesion of girlfriends and ultimately my wife, and the episodes you use for that are very different from what you’d use for a Sci fi fan, or a Dr Who fan who likes a different doctor (and let me tell you, the task was really difficult before the series was relaunched).
For example, pretty much any Moffat episode is excellent and should appeal to any right thinking Sci fi fan. But quite a few of them are unusual and don’t particularly represent how the show normally is, not to mention aren’t necessaily accessible to a newbie (Blink in particular).
Enough wibble though, here are my thoughts.
Hartnell.
Like most people I’ve seen very little Hartnell and if we’re honest most of it doesn’t work very well to a modern audience. A properly representative episode would probably be a ponderous historical ramble over eight episodes.
So I’m going to vote for ‘The Daleks’ here, as lets be honest that’s the one that kicked the whole phenomenon of Dr Who off. If it worked in the 60’s, it probably has the best chance of working now.
Troughton
I love a lot of the Troughton stories from reading them in the Target books, but as with Hartnell a lot of this when seen on TV doesn’t work particularly well to a modern audience.
I’d say Tomb of the Cybermen is probably a good choice here. It has so many of the classic Who elements (base under seige, people with a hidden agenda, Doctor as a suspect, double and tripple cross, running up and down corridors) that its a good amabassador for what this era was about.
Pertwee
Things get easier now as this era is much more accessable to a modern audience.
I’d plump for ‘Auton Invasion’ as it pretty much sets up the show from first principles and doesn’t assume any knowledge of existing continuity.
Tom Baker
Now we’re spoilt for choice, but it’s a no brainer for me.
Robots of Death, until the new series came along this was usually my first choice as a general introduction to Who. Simple, accessible story with good production values. Very easy to enjoy as a non-fan. “Please don’t throw hands at me”
Davidson
Hmm, not so easy now as there was lots of continuity and overly-complex stories starting to float about in this era. There are also less stand out excellent episodes.
The Five Doctors is tempting (and has been my other choice as a general intro in the past), but isn’t properly a Davidson story.
I’m going to indulge myself and say Resurection of the Daleks, as it’s a personal favorite. But its a pretty tough episode for a newcomer and ends on a downer.
Colin Baker
Hmm, you’re looking for the best of a bad bunch here.
Let’s say Attack of the Cybermen, it has it’s issues but is pretty action packed. Far too much continuity though. But if in doubt falling back on the Daleks or Cybermen is usually a good move (and revelation of the Daleks is a bit kooky)
McCoy
Actually one of my favorite Doctors, but he was generally hamstrung by appalling stories.
Easy choice, Rememberance of the Daleks, IMO one of the best DW stories ever. Lots of understated continuity nods for the fans, but easily accessible and fun to follow for lay folk. Plus the biggest explosion ever in old Who! You gotta love the special weapons Dalek (I’d love to see that come back in new Who)
McGann
Well there is only the Movie! Not high on the list of things I’d show anyone.
Ecclestone
Hmm, not many to choose from but some great examples.
I’d probably go with Rose, as it assumes nothing and sets everything up from scratch. As with ‘the Daleks’ forty odd years earlier this is what got the whole show off the ground again so that speaks volumes.
Tennant
Hmm, difficult actually, as most of my favorites episodes are Moffat stuff which aren’t necesarily good examples. e.g. Blink is brilliant but can’t be said to be representative of ‘normal’ who. In fact most of the best Tennant episodes are atypical, Human Nature being another example. You also have to watch out for RTDs increasing tendancy for massively overbown stories that are riddled with continuity and impenetrable to a newcomer.
So, given all that I’m going to plump for 42, a nice solid self contained story that rattles along well and is a good example of Tennant in his prime.