Do we "deserve" our bad fortune? If I recall correctly, the term karma is used to explain the concept of dependent origination and how one thing leads to another, consequently creating every event that happens in our lives. It is also emphasized in Buddhism that we should conduct wholesome deeds to obtain good karma, which will lead to good things as a result.

However, when we face unfortunate events like natural disasters and terrorist attacks, can karma explain the causes of these events and why seemingly innocent people suffer because of it? Furthermore, if we accept the notion that karma is behind everything in our lives, is that equivalent to saying those who die in these unfortunate events DESERVE it?

Much appreciated.
In the Sivaka Sutta (quoted below), the Buddha stated that some events that happen to us are a result of karma. But other things are caused by other causes including bile disorders, phlegm disorders, wind disorders, change of climate, careless behaviour, assault etc. The belief that all that happens to you is due to past karma is contradictory to Buddhism.

Elsewhere in the suttas, we find the Jain belief that in order to become liberated, one has to do penance to "burn" accumulated bad karma. This is contradictory to Buddhism.

Another belief that is contradictory to Buddhism is that karma is a system of universal justice, whose purpose is to mete out punishment on the wicked and reward the good.

In Buddhism, karma is the expression of our volition. Basically, by the expression of our thoughts, words and deeds, we try to fulfill our craving towards sensual things (of the six senses including the intellect), and to fulfill our craving towards becoming something. This is our response to greed.

However, if we do not receive what we crave after, or if what we are enjoying is suddenly taken from us, we may become angry or unhappy. In this case, we may express our thoughts, words and deeds as a reaction to our aversion.

In general, how we think, talk and act, would somehow influence our future. It's not hard to see how that works. If we act virtuously, the world responds to us positively and vice versa. It's not like if I donate exactly 10 dollars, in future, somebody will give me exactly 10 dollars in return (or the equivalent future value). Rather, it's like if I am a kind person who likes to help people, this will attract other kind and helpful people to trust me and help me too. And similarly for bad karma.

If you intentionally knock your head on the wall, you will feel pain. That's karma too.

If a change in climate causes you to catch a cold, that's not karma. That's just caused by a change in climate.

The result of karma and the result of other causes, based on the Sivaka Sutta, seem to be quite "natural" and in accordance with our experience of the world.

Of course, the "supernatural" aspect of the result of karma is rebirth. But we should not care too much about how we were born into our present life. That's not skillful or useful. What is skillful or useful is to use our volition to minimize suffering and increase happiness in future.

Also, it's useful to think of rebirth not as the rebirth of a person, but rather, as the continuation of suffering that can be ended only by Nibbana, and not by physical death.

As written by Thanissaro Bhikkhu in "To Suffer Is an Active Verb":


  This is one of the reasons why the Buddha doesn’t have us try to go
  back into the past and ask, “What did I do to deserve an illness, a
  mental state, a situation in life?” He said that if you tried to trace
  all those things back, you’d go crazy. In fact, he said, you can’t
  trace back and find a beginning point for the ignorance that underlies
  suffering. But you can see what you’re doing to sustain it now.


The Sivaka Sutta:


  Moḷiyasīvaka:
  “Master Gotama, there are some ascetics and brahmins who hold such a
  doctrine and view as this: ‘Whatever a person experiences, whether it
  be pleasant or painful or neither-painful-nor-pleasant, all that is
  caused by what was done in the past.’ What does Master Gotama say
  about this?”
  
  Buddha:
  “Some feelings, Sīvaka, arise here originating from bile disorders:
  that some feelings arise here originating from bile disorders one can
  know for oneself, and that is considered to be true in the world. Now
  when those ascetics and brahmins hold such a doctrine and view as
  this, ‘Whatever a person experiences, whether it be pleasant or
  painful or neither-painful-nor-pleasant, all that is caused by what
  was done in the past,’ they overshoot what one knows by oneself and
  they overshoot what is considered to be true in the world. Therefore I
  say that this is wrong on the part of those ascetics and brahmins.
  
  “Some feelings, Sīvaka, arise here originating from phlegm disorders …
  originating from wind disorders … originating from an imbalance of the
  three … produced by change of climate … produced by careless behaviour
  … caused by assault … produced as the result of kamma: that some
  feelings arise here produced as the result of kamma one can know for
  oneself, and that is considered to be true in the world. Now when
  those ascetics and brahmins hold such a doctrine and view as this,
  ‘Whatever a person experiences, whether it be pleasant or painful or
  neither-painful-nor-pleasant, all that is caused by what was done in
  the past,’ they overshoot what one knows by oneself and they overshoot
  what is considered to be true in the world. Therefore I say that this
  is wrong on the part of those ascetics and brahmins.”