All three films are horror stories that have been labelled as "Lovecraftian" due to their common themes of humanity facing its end at the hands of an otherworldly force beyond our capability to understand. In keeping to Lovecraft's ideas, the movies follow the rationale that mankind is a tiny, insignificant part of a vast cosmos that is at best indifferent to us. These are horrors beyond our control, beyond our understanding, and which could easily wipe us from existence. We can never truly defeat them, the best we can do is contain or delay it.
The theme that really seems to run through these movies, however, is one of infection. Though only The Thing features a literal virus (at least insofar as it infects on a cellular level), the horror is always treated like one, something that needs to be contained and prevented from spreading. The catch is that unlike a regular virus, this is not one that can be treated. Instead, the fear comes from a transformation that happens as a result exposure to the "infection". It becomes something to be avoided, which becomes increasingly difficult as the "virus" spreads to more people.
With The Thing, the concern comes from an alien organism that is capable of perfectly replicating the cells of any living thing that touches it. Its noted that, at least as far as anyone can tell, one cell of the Thing is all it takes to infect a human. That cell divides and begins assimilating other cells, which in turn divide and assimilate other cells, and so on until it has taken every part of your body. Once you are infected, there is no way to cure it. The trouble is that when you're in Antarctica and the only habitable environment is a tiny research station, it's going to be harder to avoid the people who are infected, especially when you don't know for sure who has been assimilated, who has not, and who is technically still human but in the process of being assimilated.
Prince of Darkness has a more sudden transformation that occurs from the infection. This time around, it is the green fluid (which it revealed to be alive, and the essence of Satan himself). Consuming the fluid results in almost instant death, with the corpse then being reanimated as its servant. You would think it would be easy to avoid drinking an ominous green fluid, but not when it is very good at taking you by surprise and the reanimated corpses make sure to prevent you from escaping.
The point is that the infection is more than a simple virus that can be cured. When a person is infected, there is no going back. The victim of the infection is never the same once he or she is exposed. Instead, they fall under the control of a greater influence, becoming "assimilated" in a way (literally in the case of The Thing). With each infected person the power of the otherworldly force grows and becomes harder to resist.
As the thing grows, it becomes increasingly clear that the horror can never truly end, leading to the ambiguous endings of each film. In The Thing R.J. MacReady is eventually forced to face the fact that there is no way to stop the Thing that allows the remaining men to get out alive. The best thing they can do is contain the Thing, after which point a best case scenario is that they will freeze to death in the snow.
There is, however, one thing that adds a layer of unease to this grim final scene. The only other known survivor besides Mac is Childs, who had up to this point been gone long enough to have been assimilated. The one possible indication that he is human is the presence of an earring since the prequel established that the Thing couldn't replicate inorganic material, but who's to say it hasn't learned from its past errors by trying to replace objects it spits out whenever possible. Some argue that Childs is wearing a different-coloured jacket from earlier, although the lighting makes it hard to tell for sure.
Prince of Darkness sees the number of protagonists decreasing at an increasing rate as more and more people are infected by the green fluid and transformed into servants of the eldritch entity that threatens to destroy our world. What doesn't help is the fact that said entity has ensured the protagonists are unable to leave (attempting to do so results in death), making it march harder to evade their infected colleagues as they multiply.
With In the Mouth of Madness, it is a fear of insanity that comes from the popularity of Cane's writing. The book is promised to drive its readers insane. As the story progresses, characters become violent, and seemingly delusional, or is it Trent who has been the crazy one the whole time? As the infection of Cane's writing spreads, it becomes increasingly difficult to comprehend the difference between sanity and insanity.