"Do you know what they call me in the ancient legends of the Dalek homeworld? 'The Oncoming Storm'. You may have removed all your emotions, but I bet that deep down in your DNA there's one spark left, and that's fear. Doesn't it just burn when you face me?"
- The Ninth Doctor
More than any other creature the Doctor has faced, none have struck fear into the characters and the audiences quite like that of the Daleks.
The appeared in the very second Doctor Who story "The Daleks" a group of war mongering aliens on the planet Skaro. When the Doctor first encountered them they were still wagging a battle with their ancient enemies the Thals; two species that shared the same planet. We later learn in "Genesis of the Daleks" that the Thals and Kaleds had been fighting for a 1,000 years using every weapon they could from knives to atomic weapons. Here we see their creation as the Kaled leading scientist Davros, himself a victim of a nuclear blast, takes the Kaleds to their ultimate form, something they were already mutating into, and builds a shell for them to survive. This shell is armed with sensors and advanced weapons, all to kill more Thals.
From here the genetically and cyber-enhanced Kaleds, now known as Daleks, spread out to the cosmos to destroy all life that is not Dalek.
While the Daleks of the old series never looked frightening, they were portrayed as such. So much so "that hiding behind the sofa when the Daleks came on" entered into the English cultural consciousness. And they have been voted the greatest monster of all time. This is even considering that the earliest Daleks rolled everywhere. There is a long-running joke that goes like "Daleks don't need to use stairs. They just level the building."
The revised new series brought back the Daleks and added the new concept of the Time War. This was a war the Daleks were in against the Time Lords. Over the course of the years we learned more and more. Like how the Time Lords and the Daleks wiped each other out. The Doctor played a major role in this War and finally how it was the Doctor that used the last weapon (The Moment) to end the war for good destroying both sides. The Time War became a focus of the new series and really made the Daleks feel more menacing.
The old series used to equate the Daleks and the Cybermen. Both evil races, both cybernetically enhanced humanoids. But it was the new series that finally brought them together and erased all notions they were on equal footing.
The Daleks are so popular they have also been the subject of two non-canon Doctor Who films (called Dr. Who here): Dr. Who and the Daleks and Daleks - Invasion Earth 2150 AD. These starred Peter Cushing as "Dr. Who" and were based on the television serials The Daleks and The Dalek Invasion of Earth, respectively.
I would argue that is was the Daleks that made Doctor Who so popular. The first story, An Unearthly Child, was good, but it wasn't great. The next story, The Daleks, while quaint by our standards today, was a real attention-getter. I will also claim that the serials The Dalek Invasion of Earth and The Chase from the First Doctor helped cement them as worthy adversaries of the Doctor. And the 4th Doctor series, Genesis of the Daleks, the one that introduces Davros, is one of the best Doctor Who stories ever.
All incarnations of the Doctor have had to battle the Daleks. Well. We never see the 8th Doctor do it, he likely did, but he also tried to stay out of the Time War. His successor, The War Doctor, battled them extensively.
If your enemy has to rise to the level of the hero then it is no surprise then that the Daleks are as powerful, and as popular as the Doctor themself.
ETA: Elena Square Eyes is also doing Doctor Who for her A to Z, but she is focusing on the new series. Today she did the Christopher Eccleston episode "Dalek." Pop over there and see what she has to say!
All images are used with permission from the BBC and are copyrighted 2023 by the BBC.