Yes, in the movie Wrath Of Khan, Spock gives Kirk a birthday present, a book. Kirk reads the first line of the work "It was the best of times, it was the worst of times." The book was a Tale of Two Cities.
In various companion novels Kirk and other characters read various books or poems.
Samuel T Cogley, Kirk's attorney from the episode Court Martial had a large collection of books, & we see Captain Picard packing books for his trip to Risa in Captain's Holiday. He at least took James Joyce's Ulysses which he considered light reading, but probably only in jest.