Over 10 times more people die in circulatory diseases than accidents (source). Nevertheless people (in general) fear accidents more than circulatory disease. There are statistically even more unlikely things that people fear, such as lightning.
What is the reason for this?
One thing that came to my mind is that these unlikely things are reported more in the media, but there must also be something else behind this.
This is a great question. There isn't a single reason for this phenomenon.
There is a genetic predisposition to certain fears. Though humans are bad at statistics, evolution is quite good at it. So if there is a benefit to having a fear response to something, whereby it increases the chances of survival to reproduction, then it is more likely to propagate. The trouble with evolution however, is that it's slow, and depends on survival to reproduction to work, which is not as relevant as it used to be. So humans are predisposed to fear snakes, heights, and lightning, because this fear increased the chance of survival in our evolutionary past. A fear of circulatory disease was not an evolutionary advantage at the time, and arguably still isn't, but in any case, evolution has not had sufficient time to catch up.
Genetics are not the only cause of fears, as learning also plays an important role. This was clearly demonstrated by the seminal Little Albert Experiment in which a fear of rabbits (very uncommon in practice) was induced in a baby through classical conditioning. This experiment is no longer ethical to replicate, but it showed that humans can be taught to fear just about anything. This results in individual differences in fears and phobias that depend on personal experience rather than objective statistical likelihood. Thus, a fear of something with immediate effects, such as failure or embarrassment, is more likely to develop through learning than a fear of something with long-term effects, such as smoking or junk food.
Classical conditioning is also important in understanding the impact of presentation - as mentioned, the way a fear is presented can influence it as well. Fears that more closely resemble or are otherwise associated with other things we already fear are more likely to take hold than abstract ones that we can't relate to. So the key to fears such as radiation, asteroid impact, or aliens, really has to do with framing them in a manner that we can understand.
The role of learning is evident in cultural differences in common fears as well. As you rightly pointed out, media plays a role in this, but importantly, media emphasizes different fears in different cultures, so it is presumably influenced by what each culture is attuned to. Additionally, fear is often used in politics and marketing, so cultural differences may be partially driven by needs and goals of government and corporations for example. This may be why - at least in developed countries - a fear of terrorism is more likely than a fear of ecological disaster for example. Similarly, an issue with market-driven news is that it tends to focus on particularly rare events, such as child abductions, shark bites, and plane crashes, making them seem more common than they are.
Many other factors, such as memory and cognitive biases, influence the likelihood of developing a particular fear, but hopefully this gives you the sense that objective statistical likelihood is not the only factor.
This is because human beings assess the probabilty of an event in a roughly proportional dependence of the emotions its imagination triggers or the emotion its experience triggered.
I have read of a study - sorry can't find the source but anyway it serves as a good illustration of my point - that people when asked will attach a higher probabilty to the event of a plane crash caused by terrorists than to a plane crash in general without specifying why. The first event will cause vivid pictures to pop into your mind, the latter is comparatively abstract.
Why do people tend to think that they systematically always arrive at the bus stop just when the bus leaves? (Or similar misconceptions of the kind "always when I ..." or "never when I ...") It's b/c when you get the bus that is normal and won't trigger much emotion. If you don't get the bus it will trigger negative feelings. Those feelings get associated with the event of missing the bus and make it seem more likely - in terms of neural activity, it is stronger.
Same goes of course for accidents vs some boring illness.
There are various reasons of why people behave like that but to answer the statement:
... people fear (in general) more accidents than circulatory disease.
It is probably because accidents are generally more violent and vulgar than circulatory diseases. Additionally, diseases in general are most likely to be preventable than accidents. Also, diseases are much likely to be treatable while accidents came with high chances of instant death.
It is probably the fear of getting an instant death.
