Common Greek Roots and Examples:
* Geo (γη, gê): earth: geography, geology, geocentric, geometry (earth measurement)
* Graph (γράφω, grápho): write: biography, autograph, graphic, paragraph, graphite
* Tele (τηλε, tēlē): far, distant: telephone, television, telegram, telescope
* Photo (φῶς, phōs): light: photograph, photogenic, photosynthesis
* Hydro (ὕδωρ, hydōr): water: hydroelectricity, hydraulic, hydrophobia, hydrogen
* Bio (βίος, bios): life: biology, biography, biosphere, antibiotic
* Logos (λόγος, logos): word, reason, study: logic, biology, prologue, psychology
* Morph (μορφή, morphē): form, shape: morphology, amorphous, metamorphosis
* Path (πάθος, pathos): feeling, suffering: sympathy, apathy, pathology, pathetic
* Phile (φιλέω, philéō): love: philosophy, philanthropy, bibliophile
* Phobia (φόβος, phóbos): fear: claustrophobia, acrophobia, xenophobia
* Cracy (κράτος, krátos): power, rule: democracy, aristocracy, bureaucracy, theocracy
Less Common but Still Important Roots and Examples:
* Anthropos (ἄνθρωπος, ánthrōpos): human: anthropology, misanthrope, anthropoid
* Cosmos (κόσμος, kósmos): order, world: cosmology, microcosm, cosmopolitan
* Helios (ἥλιος, hḗlios): sun: heliocentric, helium
* Aster (ἀστήρ, astḗr): star: asteroid, astrophysics, astronaut
* Chronos (χρόνος, khrónos): time: chronology, anachronism, chronic
This is just a small sampling. Many words combine Greek roots with other roots (Latin, for example) or affixes to create complex meanings. Looking up words in an etymology dictionary will reveal their Greek (or other) origins and how the roots contribute to their current meaning.