The idea that everything that happens is a result of kamma is a common enough wrong view to have a name in Pāḷi: Pubbekata-hetu-diṭṭhi (literally "the with-past-actions-as-cause view"). For a canonical discussion of this you could try the Devadaha Sutta (Majjhima Nikāya 101). It's a long and complex argument that is difficult to summarise, the Buddha works through a range of combinations and shows that most of them, including the view that everything that one experiences is a result of past actions, are illogical.
The main result of accumulated karma is usually rebirth, although some karma may ripen as vedanā "sensations". Karma was not, at least originally, intended to describe every little thing that happens, it was intended to explain how mental states drive the cycles of rebirth. At least one sutta, Karajakāyasuttaṃ (AN 10.219; v.299-301), argues that rebirth wipes the slate clean, but most karma theories allow for karma to ripen many lifetimes hence.
At least one text describes many different kinds of causes for misfortunes. In the Sīvaka Sutta (SN 36.21) eight different causes are summarised in a verse:
Pittaṃ semhañca vāto ca, sannipātā utūni ca;
Visamaṃ opakkamikaṃ, kammavipākena aṭṭhamī ti.
Bile, phlegm, wind, combinations of them, and regular processes;
Something disagreeable, sudden pains, and kamma as eighth.
Regular processes (utu) might be seasons, but it can also refer, for example, to the menstrual cycle. In this view a fatal car accident is not necessarily to do with karma, though where you are reborn afterwards is. Note that Bhikkhu Thanissaro has argued against this interpretation of the Sīvaka Sutta.
The point here is that old and new kamma do not override other causal factors operating in the universe — such as those recognized by the physical sciences — but instead find their expression within those factors."
However this "everything happens for a reason" (teleological) argument is weak by modern philosophical standards. It's a kin to the Christian claim that "God moves in mysterious ways" - there is a reason, but mere mortals cannot understand it. It only works in Buddhism because on the whole the conditions for an event are said to be in a past life and therefore unknown to us (until we begin to develop the three mystical skills or tevijjā, one of which is knowledge of former lives).
Karma is a very changeable doctrine. So that many modern traditions teach something different. Many Tibetan schools, for example, say that karma is responsible for everything that happens. The car accident would be the result of some action or actions in the past. I personally do not find this teaching compelling, and it has many philosophical problems.
The standard view of karma is that it determines which of the five "realms" (Hell, gods & asuras, humans, animals, hungry ghosts) you are born into, and perhaps the original circumstances of your birth. After that things unfold in their own way according to the nature of the realm and the choices one makes.