Crime is a serious problem nowadays.
The definite article is not used in this sentence with the "crime" since the word means "activities breaking the law" in general, it's uncountable in the sentence given above.
But are the following sentences correct? Can the word "apple" be used with the zero article? I suppose that it can't as "apple" is a countable noun, and the definite article before the "apple" is necessary when speaking about any particular kind of fruit.
Apple is the most common fruit in the region.
Apple is my favourite fruit.
(Should be "the apple" in both sentences.)
Please correct me if I'm wrong.