The following are books that I have read and personally recommend to fellow worshipers of the gods of Hellas. This list is ever expanding as I read new texts, so check back as often as you like. I have arranged them categorically the best I could to make it easier.
Primary source texts of hellenic religious practices and history
Hesiod, Works and Days
Strabo, the Geography of Strabo
Herodotus, The History of Herodotus
Pausanias, A Description of Greece
Plutarch, The Lives of Noble Greeks and Romans
Primary source compilations of myths and related
Apollodoros, The Library
Diodorus Siculus, The Historical Library of Diodorus Siculus
Aratos, The Phainomena, or Heavenly Displays of Aratos
Plato, The Dialogues of Plato
Plutarch, On the Delay of Divine Justice
Xenophon, the Memorbilia of Socrates
Pythagoras, the Golden Verses of Pythagoras
Proclus, On the Theology of Plato.
Pindar, The Poetry of Pindar
The poetry of Kallimachus
Hesiod, Homeric Hymns
The Orphic Hymns
Sappho, Poetry of Sappho
Aclaeus, The Songs of Aclaeus
Bacchylides, The poems and fragments of Bacchylides
Theocritus, The Idylls of Theocritus
Epic Poetry and other long poems
Homer, The Iliad
Homer, The Odyssey
Hesiod, The Sheild of Herakles
Apollonius of Rhodes, the Agronautika
Plays: Comedies and Tragedies
Aeschylus, The Oresteia
Aeschylus, Prometheus Bound
Aeschylus, Seven Against Thebes
Aeschylus, The Suppliant Maidens
Aeschylus, The Persians
Euripedes, The Bacchants
Euripedes, Iphigenia at Aulis
Euripedes, Iphigenia among the Taurians
Euripedes, Trojan Women
Brown, Richard. The Great Dionysiak Myth
Burkert, Walter. Greek Religion.
Davidson, James. The Greeks and Greek Love: A Bold New Exploration of the Ancient World
Fairbanks, Arthur. A Study of the Greek Paian.
Guthrie, W.K.C. Orpheus and the Greek Religion.
Harrison, Jane E. Prolegamena to the Study of Greek Religion. (for info, her conclusions and interpretations are not worth much imho)
Muller, C.O. The History and Antiquities of the Doric Race.
Muller, C.O. Dissertation onthe Eumenides of Aeschylus
Arnold, Irene Ringwood. Local Festivals at Delos
Arnold, Irene Ringwood. Festivals of Rhodes
Bates, William Nickerson. The E of the Temple of Delphi
Cook, Arthur Bernard. The Bee in Greek Mythology
Detienne, Marcel. Forgetting Delphi between Apollo and Dionysos
Ederkin, G.W. Dionysos Eleutheros and Liber.
Fontenrose, Joseph. The Spring Telphusa.
Haldane, J.A. Musical Instruments in Greek Worship
Harrison, Jane E. Delphika
Hendrick, Charles W. Jr. The Temple and Cult of Apollo Patroos in Athens
Howe, Thalia Phillies. The Origin and Function of the Gorgon-Head
Krappe, Alexander H. Apollon Kyknos
Krappe, Alexander H. Apollon Onos
Krappe, Alexander H. Apollon Smintheus
lloyd-Jones, Hugh. Artemis and Iphigenia
Long, Charlotte R. The Gods of the Months in Ancient Art
Oppe, A.P. The Chasm at Delphi
Rigby, K.J. The Schedule of the Eleusinia
Robertson, Noel D. Two Processions to Eleusis and the Programs of the Mysteries. Seaford, Richard. The Eleventh Ode of Bacchylides: Hera, Artemis and the Absence of Dionysos.
Sourvinou-Inwood, Christiane. The Myth of the First Temples at Delphi.
Thomson, George. The Greek Calendar
Vurtheim, J. The Miracle of the Wine at Dionysos’ Advent; On the Lenaea Festival.
The Oxford Classical Dictionary (compiled by Simon Hornblower and Anthony Spawforth)
The Dictionary of Greek and Roman Antiquities (compiled by William Smith)