Here's a list of some of the services besides the Divine Liturgies of Sts. Basil the Great and John Chrysostom.
Daily Office: Found in the Horologion. 8 prayer services, starting with Vespers at sunset, usually observed only in monasteries. Parishes use parts of the Daily Office when they hold Vigils, etc.
Royal Hours: All of the hours at once, along with the Psalms from the Typika and other special prayers. These are read on Holy & Great Friday, as well as on the eve of the Feasts of Christ's Birth and Theophany.
Various Holy-Week-Only Services: Many liturgical customs -- even whole blocks of services -- are unique to Holy Week. No time to list them all. Fr. Calivas wrote a whole book on them.
Divine Liturgy of the Presanctified Gifts: Celebrated on weekdays during Great Lent. In U.S. parish practice, Wednesday & Friday, but can be done every weekday. It is an ancient Liturgy, which consists of Vespers, several special prayers/chants, and Holy Communion. Since weekdays in Lent are supposed to be times of somber reflection, there is no Anaphora/Consecration (a prayer of thanksgiving & jubilation). Rather, the priest uses bread that he consecrated, intincted and set aside during the previous Sunday's Divine Liturgy. According to Tradition, St. Gregory the Dialogist, Pope of Rome in the 6th century, wrote the Liturgy. Recent scholarship suggests he wrote it down after witnessing it in Constantinople, where it had already been practiced for some time.
Great Canon of St. Andrew of Crete: A lengthy 7th century poem about repentance. Chanted during Great Lent at various times, depending on tradition, usually during the first week of Great Lent (considered to be the strictest fast/week of repentance). Often, it is chanted in parts during the first week's Great Complines, another Lenten service (see below).
Great & Small Compline, or Apodeipnon: Literally, the "after-dinner" service. Some scholars ascribe its original form to St. Basil the Great. It consists of Psalms, prayers and usually at least one Canon, read after dinner. Small Compline is read every day in monasteries and, depending on the speed and number of Canons, take 20 to 45 minutes. Great Compline is another beast, really. It is longer and penitential in nature -- and thus celebrated during Great Lent (and, in monasteries, as part of Vigil). Unlike Small Compline, which is merely read, it has several chanted portions (e.g. "God is With Us", "Lord of the Powers"), as well as some unique features (e.g. Prayer of Manasseh, from the Septuagint). In Greek parish practice in the U.S., Great Compline is often observed at least once a week during Great Lent. In the first week of Lent, is is also the service during which one chants the Canon of St. Andrew.
Great & Small Blessing of the Water, or Agiasmos: Always observed on the eve of the Feast of the Epiphany and on the feast itself. Some U.S. parishes, following the practice of Holy Cross Greek Orthodox School of Theology and some Greek monasteries, celebrate the Small Blessing of Water on the first day of every month. It is also customary to celebrate the Small Blessing at the "inauguration" of various things (e.g. beginning of school year, opening of a building, etc.). It is also customary for the priest to bless with holy water the home of every parishioner after Theophany. Often times, depending on the number of homes to be blessed, the priest & family will celebrate at least a good portion of the Small Blessing in the home itself.
The Blessing of Five Loaves of Bread, or Artoklesia: Usually done during a Vigil, or, in Greek parish practice in the US, during Great Vespers on the eve of major feast. It's a distinct service of thanksgiving, however, in which one blesses five loaves of sweet bread, along with representative samples of wheat, wine and oil.
Moleban/Paraklisis to Various Saints: Many exist, and are chanted at any time of need.
Anointing of the Sick: The whole liturgical service, including the Gospel and Epistle readings, is done whenever needed. Also, in Greek practice, on Wednesday of Holy Week.
Akathist Hymn: Nowadays, there are many Akathists. They are all modeled after THE Akathist Hymn to the Theotokos, a Byzantine poem written in the 6th century. This original Akathist is chanted as part of the Salutations, or Chairetismoi, service during Fridays in Great Lent -- at least in the Byzantine/Greek/Arab tradition. Don't think the Slavs do it.