There aren't any bad stories here, but there is a certain looseness in adhering to the criteria of the title. We have stories where man has vanished all together, stories where man has evolved, stories where the modern world has been apocalyptically transformed, and stories showing that transformation in progress and one story that is none of those.
I suspect the collection started out as an updating of the classic anthology The Last Man on Earth co-edited by Greenberg. The volumes share many stories, and Silverberg's learned introduction about the history of the disaster sub-genre of science fiction mentions twenty stories for the collection instead of its actual 19 with Frederic Brown's "Knock", which appeared in the former collection, actually not being here.
Because fashions in the end of the world change, I decided, rather than following the thematic groupings and order of the stories, I'll list them in chronological order of original publication.
"Kindness", Lester del Rey (1944) -- The last man on earth is retarded - at least compared to the homo intelligens which have replaced us homo sapiens. Tired of their condescension, he makes plans to escape to space.
"Flight to Forever", Poul Anderson (1950) - Anderson's story of a time traveler doomed to press ever onward into the future and see how none of man's and alien's works ever last.
"'If I Forget Thee O Earth ... '", Arthur C. Clarke (1951) - The frequently anthologized tale of man in exile from the radioactive ruins of Earth.
"The Wheel", John Wyndham (1952) - The survivors of an unspecified apocalypse are so fanatic about the threat technology poses that they even ban the wheel. But, of course, there are always a few who are interested in such things.
"The Underdweller", William F. Nolan (1957) -- The underdweller hangs out in the storm drains of Los Angeles, fearing discovery by the horrible creatures that have inherited the Earth.
"The Store of the Worlds", Robert Sheckley (1959) - More of a fantasy tale than science fiction. All your possessions will buy you the opportunity to experience your deepest desires.
"Lucifer", Roger Zelazny (1964) - The last man on Earth struggles to relight a city.
"The Big Flash", Norman Spinrad (1969) - Rock and roll and a secret Pentagon propaganda campaign get way out of hand. A tour-de-force of style with its multiple viewpoints.
"When We Went to See the End of the World", Robert Silverberg (1972) - Unlike the other stories from the 1970s here, this one doesn't feature nuclear war. But there is plenty of other mayhem - presidential assassinations, plagues, and earthquakes. But it's the real and final end of the world the resolutely trivial partygoers of this farce care about.
"Jody After the War", Edward Bryant (1972) - The subtle physical and psychological damage a limited nuclear war has wrought on a man's lover.
"Dark, Dark Were the Tunnels", George R. Martin (1973) - Five hundred years after a nuclear war, some explorers from the moon come across what man has become in the ruins of the New York City subways.
"The Feast of Saint Janis", Michael Swanwick (1980) - The weakest story in the book. It's hard to believe that, even in 1980, Janis Joplin was really popular enough to imagine her the centerpiece of a strange, annual rite in a ruined America. Ignore that bit of Baby Boomer silliness, and it's an interesting echo of Fritz Leiber's "Coming Attraction" and Norman Spinrad's "The Lost Continent".
"Salvador", Lucius Shepard (1984) - One of Shepard's tales of warfare in a near future Central America. A good story but in no way does it conform to the book's stated theme.
"Storming the Gulf", Gregory Benford (1985) - A nuclear war limited by a version of the Strategic Defense Initiative, but there is still much horror around the Gulf Coast for survivors in this Faulknerian tale.
"Salvage", Orson Scott Card (1986) - A rootless young man thinks there may be a treasure in the mostly submerged ruins of the Mormon Temple in Salt Lake City.
"We Can Get Them for You Wholesale", Neil Gaiman (1989) - Another fantasy tale, this time about a bulk purchase that gets seriously out of hand.
"Afterward", John Helfers (2006) -- Not really a story but a detailed, evocative account of the Earth 3000 AD in the aftermath of a massive impact event.
"The Hum", Rick Hautala (2007) - The world ends due to a really annoying noise. A bit of a gimmicky ending.
"By Fools Like Me", Nancy Kress (2007) -- Kress nicely plays around with the sympathies of her readers in this tale of understandable environmental fanaticism versus the love of literature.
So, a couple of fantasy-like stories, one story that really doesn't belong, and an unconvincing use of Janis Joplin dilute the pure end-of-the-world science fiction experience, but, overall, a good addition to the apocaholic's library.