The Eastern Catholics are one of the Church’s best kept secrets and most Catholics would give funny looks if anyone mentioned words like "Maronite," "Chaldean," or "Melkite." And yet, these groups are all fully Catholic, meaning professing the whole of the Catholic Faith and  being in communion with the See of Peter. A Roman Catholic can (and should) visit these churches and can receive communion. Technically, when we in the West speak of Catholicism, most of us mean "Roman Catholicism" because we are talking about our experience in the Roman Rite. The Eastern Catholic Churches do not use the liturgy of the Roman Rite, but their own unique liturgies. Most of them are similar to the liturgies of the Orthodox Churches.

The Eastern Catholic Churches are an asset to the Catholic Church. Why? Because one of the marks of the Church is its catholicity. The Catholic Church wouldn’t be very catholic or universal if it were only a Western Church. Because of the Eastern Catholic Churches, our claim to catholicity is verified and strengthened. No other Christian group, no matter how many diversity related buzzwords they may use, can claim the cultural and geographical diversity of the Catholic Church.

The Eastern Catholic Churches are also a way in which those in the Roman Rite can deepen our spiritual experiences. The wealth of the East, practice and theological emphasis, is available to the Western Church via the Eastern Catholics. It’s also great to know that as Catholics we have not settled into a Western cultural ghetto, but can totally embrace our Eastern brothers and sisters as fully Catholic, even though they are ethnically and culturally different and have different liturgical practices and varying customs. I am attending a Byzantine Catholic parish tomorrow and wanted to give a brief introduction since I will probably write about my experience there soon.

Here is a list of the Eastern Catholic Churches, divided by their general geographical settings:

Alexandrian:
Coptic (not to be confused with the other Coptic Church, which is not in communion with Rome)
Ethiopian

Antiochian:
Syrian
Maronite
Malankar

Armenian:
Armenian

Chaldean:
Chaldean
Malabar

Byzantine:
Byelorussian
Bulgarian
Greek (not to be confused with the Greek Orthodox Church)
Hungarian
Italio-Albanian
Melkite
Romanian
Ruthenian
Slovak
Ukrainian
Krizevei
Albanian
Russian (Not to be confused with the Russian Orthodox Church)

Sources/more information:
The Eastern Catholic Churches
Eastern Catholic Churches