Here is a list of some of the saints called upon for special purposes, but it certainly isn't exhaustive.
To Have a Child
St. Anna, Mother of the Theotokos
St. Elizabeth, Mother of the Forerunner
St. Sabbas the Sanctified of Palestine
St. Irene Chrysovolantou
St. Symeon the Myrrh-streamner, father of St. Sava of Serbia
For Safe Childbirth
St. Eleutherios
For the Care and Protection of Infants
St. Stylianos
For Young People
Holy Great Martyr Demetrios the Wonderworker
For Marital Difficulties
Holy Martyrs Shamuna, Guria, and Habib
Sts. Peter and Febronia of Muron (also for newlyweds)
Delivery from Sudden Death
St. Barbara the Great Martyr
Against Drinking
Holy Martyr Boniface and the Righteous Aglais
For Travelers
St. Nicholas (in general, and specifically for sea travel)
St. Jon the Russian (in general, specifically auto)
St. Niphon, Patriarch of Constantinople (for safety at sea)
For the Kitchen and Home
St. Euphrosynos the Cook
St. Sergius of Radonezh (for baking)
Sts. Spyridon and Nikodim of Kievo-Pechersk (Prosphora making)
St. Juliana Lazarevskaya
St. Prockor of Kievo-Pechersk
For Trading
St. Paraskeva
For Cobblers
St. Eustathius the Cobbler of Georgia
For Physicians
St. Panteleimon
Holy Unmercenaries
St. Agapit the Physician of Kievo-Pechersk
For Perfumers
St. Abo the Perfumer of Georgia
For Headaches
Holy New Martyr Demas of Smyrna
For Eyes
St. Paraskeva
St. Lucia of Sicily
For Ears
St. Spyridon the Wonderworker
For Teeth
St. Antipas of Pergamum
For Hernias and Intestinal Disorders
Holy Great Martyr Artemius
St. Artemis of Verkola
For Throat
St. Blaise of Sebastia
For Finding Employment
St. Xenia of St. Petersburg
For Help is Studies
Three Hierarchs: St. Basil the Great, St. John Chrysostom, St. Gregory the Theologian
St. Sergius of Radonezh
St. John of Kronstadt
St. Nestor the Chronicler of Kievo-Pechersk
St. Justin the Martyr Philosopher
For Church Chanting
St. Romanos the Melodist
St. Theodosius of Chernigov
St. John Koukouzelis
Sts. Leonty and Geronty, Canonarchs of Kievo-Pechersk
For Iconographers
St. Luke the Apostle and Evangelist
St. Alypius of Kievo-Pechersk
St. John of Damascus
For Patient Endurance of Affliction
St. Job the Much-Suffering
St. Eystanthius Placidas and Family
Holy Forty Martyr of Sebastia (especially in freezing cold weather)
Holy Forty-two Martyrs of Amorion
St. Pimen the Much-Suffering of Kievo-Pechersk
For Protection Against Thieves
St. Gregory the Wonderworker of Kievo-Pechersk
For Stone-workers
Holy Martyrs Florus and Laurus
For Soldiers
Holy Archangel Michael
St. George the Great Martyr
St. Barbara the Great Martyr
St. Titus the Soldier of Kievo-Pechersk
For Spiritual Help, Consolation, and Compunction
St. Ephraim the Syrian
St. Alexis the Man of God
St. Seraphim of Sarov
For a Good End to Ones Life
Holy Archangel Michael
St. Niphon, Patriarch of Constantinople
For Captives, Prisoners, and Court Cases
St. Onouphrios the Great
St. Peter of Athos
St. George the Great Martyr
St. Stimeon the God-Receiver
For Help is Distress, Poverty, etc.
St. Nicholas the Wonderworker
St. Martin of Tours, the Merciful
St. John the Almsgiver of Alexandria
St. John of Kronstadt
For Finding Things
St. Phanourios the Great Martyr
St. Menas the Greaty Martyr of Egypt
For Meeting a Difficult Situation, an Interview, etc.
St. David the Prophet, Psalmist and King
The Holy Unmercenaries and Healers
Sts. Cosmas and Damian of Rome, and their mother Thodoti of Asia Minor, and their brothers Anthimus, Leontius, and Evropius of Arabia
Sts. Cyrus and John of Alexandria
Sts. Panteleimon and Hermolaus
St. Mocius
St. Thallelaus
St. Domedes the Healer
St. Anicetus
St. Julian the Martyr
St. Zotious the Orphan-Keeper
St. John of Kronstadt
St. Nectarios of Aegina
Holy Archangel Raphael
For Animals and Livestock
St. George (cattle and herds)
St. Modestus of Jerusalem
Holy Martyr Mamas
St. Parthenius of Radovysdius (cattle)
Sts. Spevsippus, Elesippus, and Melevsippus (horses)
St. Tryphon (geese)
For Protection of Crops from Pests
St. Michael of Synnada
St. Gerasimos the New Ascetic
For Protection of Gardens from Pests
Holy Great Martyr Tryphon (also for hunters)
Against Demonic Influence and Witchcraft
Sts. Cyprian and Justina
St. Theodore Sykeote
St. Mitrophan of Voronezh
For Chastity and Help in Carnal Warfare
St. John the Forerunner
St. Demetrios the Great Martyr
St. Moses the Hungarian
St. John the Much-Suffering
Holy Martyr Theodore the Byzantine
Holy Martyr Ignatios of Athos
St. Thomais
St. Martinian
St. Basil of Mangazea
St. Mary of Egypt
St. Joseph the All-Comely
St. Susanna (Old Testament)
St. Anysia the Virgin Martyr
For Mental Disorders
St. Naum of Ochrid
St. Anastasia
St. Gerasimos of Cephalonia (the possessed)
Against the Plague
St. Haralambos
St. Marina the Great Martyr
St. Bessarion the Saviour, Archbishop of Larissa
For Help Against Quick-temper and Despondency
St. Tikhon of Zadonsk
For Workers in Hospitals
Holy Unmercenaries
St. Dositheus, Disciple of Abba Dorotheus
For Guilelessness and Simplicity
Holy Apostle Nathaniel
St. Paul the Simple