The appeal of the Daleks is a matter which is often discussed, both in Who fandom and in the mainstream media. I have some thoughts on this matter!
On a superficially level their importance to the modern era of Who (and much of the classic era) is that you know full well shit is gonna go down when the Daleks are around. By and large their schemes are big and bold. Moreover they are normally a good match for the Doctor. Partly because they stand in clear opposite to him on a moral level, but also because they almost always fight from a position of strength. They are not normally portrayed as generic bad guys wanting the earth for no clearly definable reason. Generally they have a plan and an army and several conquered planets/ solar systems/galaxies already one before the Doctor shows up on the screen. Thus the stakes are always that bit higher.
But this does not explain their appeal from the earliest days of the show. Indeed it is only because they were so popular that they ever got to be the top dogs amongst the shows bad guys. So there must be more to it than the prospect of the Doctor and the Daleks fucking each others shit up.
Obviously the design of the beasties is a key feature. For a start off they are clearly not humanoid. I think this is a big deal. When you think back to their introduction in 1963 they were unlike anything that had come before. Even the likes of “Robbie the Robot” from “Forbidden Planet” was essentially humanoid in appearance. There is resembling a human in the Dalek form. Yet as with many features in Doctor Who there is an element of the mundane, the domestic. The familiar sink plunger arm and egg whisk gun are entirely familiar. But it is this very familiarity which helps embellish the uniqueness of their appearance. There is a fundamental incongruity about these common household objects being analogous to limbs.
Sylvester McCoy has likened the appearance of the Daleks as being tank like. There is something in this (particularly the armoured bling models of the current era). Squash a Dalek flat and you would have something that looks very similar to a tank. Similarly the old style extermination effect is reminiscent of a nuclear flash.
The voice is also an essential factor. The voice of a Dalek is harsh, grating and filled with hate (and often screaming Exterminate!). The voice also ties in with another design feature. That being the flashing lights on the top of the Dalek's casing. There has never been any on-screen explanation for this. To the best of my knowledge there has been no explanation in any of the audios, books or comics either. However, I love the explanation offered by Terry Nation in a book in the 70s. The explanation was that the lights were a way for the Dalek to discharge energy and that without them the Dalek would basically explode from the pent up energy of its own hate and anger. This strikes me as being a fantastic explanation and would also explain why the more senior Daleks have had more lights and/or bigger casings, it would allow for more room for the pent up energy and more discharge of that energy.
Important thought these features are, I think people are most attracted to the mythos of the Daleks. The Daleks were the creation of Terry Nation and they neatly encapsulate two regular themes of Nation's writing. The first of these theme's is that of Fascism. Nation was a child of the second world war and would return throughout his career to the examination of the Nazi regime; Blake's 7 was a series based almost entirely around this fascination. The Dalek's were the other main examination of the Nazi's. The second theme is that of nuclear war. Nation created the series Survivors as an examination of the risks of a nuclear catastrophe.
At the time the Dalek's story first aired (1963) these concerns were very much mirrored by the population of the UK. Much of the population were alive during the second world war and for many the history of that event was very much prevalent in their minds. Similarly the risk of a nuclear war was a pervasive fear following the nuclear bombing of Japan and with the (then) recent Cuban Missile crisis, the assassination of Kennedy, the cold war and the prospect of war in Vietnam.
These twin themes of fascism and a nuclear winter were developed during the first two Dalek stories and have underpinned every Dalek story and the perception of the Daleks ever since. In the first appearance in 1963 (only the second Doctor Who story) the nuclear winter theme was by far the more prevalent. We learn that the Daleks were mutants born out of a nuclear catastrophe. Even at this early stage there was a clear public fascination for the Daleks was clear. However, it is most likely the second Dalek story that cemented their role in Doctor Who and indeed the popular culture of Britain itself.
That story was the Dalek Invasion of Earth and although it is actually a pretty rubbish story; it is arguably the most important story the series ever did and also features a number of iconic, classic, scenes (albeit interspersed with entire episodes where nothing happens). In essence the story is the Blitz transposed to the future. The Daleks are a mythologised version of the Nazi's and are primarily interested in invading (in apparent order of importance): London, the home counties, the British Empire, then all the rest!
The first volume of the About Time series (an excellent series by Lawrence Miles and Tat Wood) puts it perfectly:
[the Daleks] routinely use the verb “exterminate” to mean killing individuals, not groups or races. Yet the idea or mass extermination is present, and one of them calls it a “final solution”. Earlier we see them giving fascist salutes with their sink-plungers, employing slave labour camps...and broadcasting propaganda over the airways. They've apparently wiped out all non-white races on Earth... and believe themselves... racially superior. We believe there may be a subtext underlying all of this!
Clearly this subtext would have resonated with the population of Britain at the time comprised, as it was, of those who had lived with through the war and those who lived with the legacy of the war (be it deceased or injured relatives or the cultural recollection of the war).
The Daleks as Space Nazi's becomes a simple fact of their existence from this point onwards. Indeed in the following Dalek stories (The Chase, The Dalek Masterplan, The Power of the Daleks) it is simply taken as a given that this is the very essence of what the Daleks are about. In the Evil of the Daleks the fascistic nature of the Daleks once again becomes a key plot point again as they undertake a series of what are, in essence, experiments in eugenics to discover the “Dalek” and “Human” factors.
Again in The Day of the Daleks, they are back in control of the Earth, operating “work camps”. Interestingly they are only able to colonise the Earth following a world war between the superpowers of the Earth (note the use of the nuclear war again). They also maintain control of the planet by use of a combination of human sympathisers and a slave race (the Ogrons).
The remaining Pertwee Dalek stories sees them used in a rather unsatisfactory manner. In Planet of the Daleks and Death to the Daleks they are simply generic bad guys. However they were back in form in Genesis of the Daleks. As the name implies this story shows us the creation of the very first Daleks. And wouldn't you know it they arise from a bunch of (human) Nazi's who are in the middle of a nuclear war! This story also introduces us to Davros, the creator of the Daleks and a rough mixture of Hitler, Goebbels and Himmler. Genesis shows us that the fascist philosophy of the Daleks is a product of their genetic make up and their environment and culture.
Dalek appearances after Genesis are much less frequent than was the case before Genesis. However it is notable that the last two Dalek stories of the classic era, Revelation of the Daleks and Remembrance of the Daleks, see the Daleks at civil war. Although this arguably weakened them and alienated the casual viewer; it was a development that was entirely in keeping with the themes established from the earliest stories. It is only natural that a second generation of Daleks would view the first as being inferior and aberrant (and vice versa). Similarly it is only natural that each Dalek race would seek to purify their own species before moving onto dealing with the rest of the universe.
The Daleks were a part of Doctor Who that somehow remained ubiquitous throughout the wilderness years between 1989 and the revival in 2005. They even made smurf like cameo in McGann's one off! The return of the Daleks (or risk that they would not return) were a regular talking point up to the airing of season one in 2005.
But the more interesting question for me at the time was how the Daleks would return. Happily Russell T Davies is a very clever bunny. In the episode Dalek they are immediately re-established as Nazi-Killing machines! Indeed that lone Dalek probably kills more people on screen in one episode than were killed by Daleks in the entire classic era. The reason being that it genuinely believes they should die.
Looking back you get the impression that RTD wasn't entirely sure that a new generation would “get” the Daleks. Thus the traditional fascism is tinged with modern day religious fundamentalism and self loathing (over their impure genetics) for the season one finale. As it happens this was an unnecessary, albeit fitting, embellishment. People DID get the Daleks on an instinctive level.
The last appearance of the Daleks was in the recent Stolen Earth/Journey's end season finale. Once again the Daleks were taking the usual party line, only this time turned up to 11! We the wiping out of all other species in the entire cosmos by way of a “reality bomb” (read nuclear explosion).
So pulling all of this together; why are the Dalek's so popular? The answer is “all of the above”. The Dalek's resonate with us on an almost primal level because they are an archetypal representation of humanity at its worst. The design and mythology of the Daleks are reminiscent and reflective of the worst incidents of human history (the holocaust), the darkest hours of British history (World War 2 and the Blitz) and our fears of what we are capable of in the future (nuclear Armageddon).