The Last Policeman by Ben Winters. It is not like the Sci-Fi suggestions above but I really enjoyed it. Would you still do your job if everything was ending in 6 months (due to an asteroid)? The sequel,
Countdown City is out, too. The End of the World meets Noir.
Oooooh, oooooh!
The Children of Men by P.D. James!
The Not Yet by Moria Crone. Dystopia set in New Orleans! Highly recommended.
Good Omens by Neil Gaiman and Terry Pratchett!
The Handmaid's Tale by Margaret Atwood.