If you want an omnibus of short fiction by Arthur C. Clarke, a Science Fiction Writers of America Grand Master, then you want The Collected Stories of Arthur C. Clarke. If you're looking for a representative sample of Clarke's short stories, or for some examples of the creative and extrapolative abilities that established Clarke as one of science fiction's greatest and most important writers, then check out Tales from Planet Earth.
Tales from Planet Earth ranges widely across time, but the stories are centered on our home world. Many SF writers confine their visions of earth to its flatlands, but Clarke is three-dimensional; his stories "Hate," "The Deep Range," and "The Man Who Ploughed the Sea" plunge into the ocean, while "The Cruel Sky" ascends the Himalayas. Some stories, like "The Other Tiger" and "'If I Forget Thee, Oh Earth...'," end on chilling twists. "The Road to the Sea" spans centuries and millennia to explore how humanity's exodus to the stars may affect the world left behind. "Hate" considers how transcendence of the Earth's atmosphere may affect ancient enmities. "The Parasite" demonstrates a scary nastiness not usually associated with Clarke. "The Wall of Darkness" is set on an alternate-universe earth so different from ours, and "The Lion of Comarre" is set in a future so far away, that both stories feel like fantasy; but both are rigorously extrapolated from scientific theory. Two lighthearted entertainments, "The Next Tenants" and "The Man Who Ploughed the Sea," are from Tales of the White Hart. All of the stories in Tales from Planet Earth are recommended.

The iBooks 2001 Anniversary Edition of Tales from Planet Earth collects 14 SF stories first published between 1950 and 1987, including the satire "On Golden Seas," which has "never before [been] collected in any Clarke book." --Cynthia Ward

Review
"Here...is a collection of Arthur's science fiction stories, science fiction dealing with science, extrapolated intelligently. How you will enjoy it!" ISAAC ASIMOV"
Product Description
The fiction of Arthur C. Clarke has spanned the universe. He has carried us across unimaginable distances to alien times and places. Yet he has not lost sight of his home. Many of his greatest stories are set-or have their roots-right here on Planet Earth. In this book, Clarke's best stories about our home planet are gathered together. For Arthur C. Clarke, more than any other science fiction writer, "home" is the entire Earth, through all of space and time. In this book, he shows us around his home to share his wonder. He invites us to share his vision and his dream.

About the Author
Arthur C. Clarke is the author of many seminal works of science fiction, most noteably; 2001: A SPACE ODYSSEY (Little Brown).