Here is list of things to which we owe a debt to Ancient Greece. Sometimes they were the inventors and on other occasions they made important innovations. Despite the Greek reputation for being impractical you will see many of them were extremely functional.
Abstract Math
Antikythera Mechanism (an ancient mechanical computer designed to calculate astronomical positions)
Architecture
Art
Astrolabes
Astronomy
Automatic doors
Cannons
Catapults
Central Heating
Coins
Cranes
Democracy
Diving Bells
First Alphabet With Vowels
Geometry
Hippocratic Oath
History
Levers
Lighthouses
Logic
Medicine
Mythology
The New Testament
The Olympics
Philosophy
Physics,
Pipe Organs
Pulleys
Rhetoric
Sculpture
Showers
Steam Engines
Theatre – Tragedy and Comedy
Trial By Jury
Vending Machines
Wine