At the Ruthenian Byzantine Catholic Church that I attend regularly (yet baptized/confirmed Roman), we have been studying the Divine Liturgy. Some interesting information is that the different rites, although some translate the Divine Liturgy into other languages, use a small number of liturgies. Mainly they vary with different Anaphora.
Byzantine
Liturgy of Saint Basil
Liturgy of Saint John Chrysostom
Liturgy of Presanctified Gifts
Armenian
Liturgy of Saint Gregory
Alexanderian
Liturgy of Saint Basil
Liturgy of Saint Cyril (Saint Mark)
Liturgy of Saint Gregory
Antiochene
Liturgy of Saint James
Chaldean
Liturgy of Mar Addai & Mar Mari
Liturgy of Mar Theodore of Mapsuestia
Liturgy of Mar Nestorius
Roman
Roman Ordinary Form
Roman Extraordinary Form (Latin)
Ambrosian
Mozarabic
Braga
Carthusian
Benedictine
Regular Orders (various, e.g., Carmelite)
Anglican Use
This list may vary because some sources list extinct liturgies.
In the United States of America, the largest Eastern Catholic church memberships are (2008 Annurario Pontifico):
- Chaldean 26%
- Ruthenian Byzantine 18%
- Syro-Malabar 16%
- Maronite 14%
- Ukrainian 11%
- Armenian 7%
- Melkite 5%
- Syrian 2%
- Romanian Greek 1%
- Russian (under Latin protection)