It can be used in both ways, as a countable and as an uncountable noun:
There was a terrible famine in Ireland in the late 1840s and early 1850s that killed an estimated one million people.
(Countable: one particular event, in one place and at one time.)
Throughout history, famine has been a persistent problem in many parts of the world.
(Uncountable: the general condition, in many places and at many times.)
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