Stephen King's THE STAND ("presents a detailed vision of the total breakdown of society after the accidental release of a strain of influenza that had been modified for biological warfare causes an apocalyptic pandemic, killing off over 99% of the world's population.") Includes metaphysical/religious elements; Good vs. Evil. The book is HUGE. A made-for-TV movie exists, but hasn't aged very well (and wasn't super great to begin with). A remake is in the works.
Joe Hill's THE FIREMAN ("A mysterious fungus has appeared and it is infecting people. This infection causes people to spontaneously combust and society must deal with the fallout of this event.") Not a virus per say, but still a contagion. Focus on human relationships.
Emily St. John Mandel's STATION ELEVEN (The novel takes place in the Great Lakes region after a fictional swine flu pandemic, known as the "Georgia Flu", has devastated the world, killing most of the population.") Hear good things about it.
Max Brook's WORLD WAR Z: AN ORAL HISTORY OF THE ZOMBIE WAR ("a collection of individual accounts following the devastating global conflict against the zombie plague. Brooks used World War Z to comment on government ineptitude and US isolationism, while also examining survivalism and uncertainty.") Also a movie. Hear good things about it.
Ling Ma's SEVERANCE
The BBC's Survivors (remake of the 1975 original, this 2008 reboot "depicts the lives of a group of people who survived a virulent unknown strain of influenza which has wiped out most of the human species.") The show was cancelled before its time but the two seasons are still worthwhile viewing. The only monsters in this are other people vying for dwindling resources/power over one another.
28 Days Later ("The plot depicts the breakdown of society following the accidental release of a highly contagious virus and focuses upon the struggle of four survivors.) The "virus" results in a violent 'rage-sickness'—lots of blood and gore. Same for the sequel, 28 Weeks Later. Not for everyone.
Outbreak ("A dangerous airborne virus threatens civilization in this tense thriller.") Classic 1995 film starring Dustin Hoffman, Morgan Freeman, and Rene Russo. Like Survivors, this movie attempts a 'realistic' portrayal (for a movie) of a viral outbreak and its consequences (though this, at least, has a happy ending with a cure).
The Last of Us ("Twenty years after a fungal outbreak ravages the United States, transforming its human hosts into aggressive creatures known as the Infected, civilization has been decimated. Survivors live in heavily policed quarantine zones, independent settlements, and nomadic groups.) TLoU's plot focuses on human relationships and what we're willing to do for (and to) one another to survive. Hailed as a milestone in video game storytelling. It's also fun as heck to play. A sequel game is soon to be released and a TV show is in the works (announced this week).