Yes, there are still Orthodox churches, and they go by "Orthodox Church," although in western countries this may often be preceded by the ethnicity of the founders of the parish - "Greek Orthodox," "Antiochian Orthodox," "Russian Orthodox," etc. A list of the canonical orthodox churches of the world can be found at http://aggreen.net/autocephaly/autoceph.html
Haredi Jews are ultra orthodox Jews found around the world.
The Orthodox Church as it is today was established at the Great Schism of 1054, when Christianity split into the East (Eastern Orthodoxy) and the West (Roman Catholicism).
Orthodox, Conservative, and & Reformed.
The major Eastern Orthodox countries are Greece and Russia. Eastern Orthodox denominations also have significant followings in Serbia, the Middle East and in Egypt, as well as a world-wide diaspora.
If your question is "Why did Jesus Christ found the Orthodox Church", he founded the Church so that we can continue his works here on Earth after his departure.
Russian orthodox. Greek orthodox. Coptic orthodox. Antiochia orthodox. Eastern orthodox. Ethiopian orthodox.
Yes, but the Orthodox look at a different calendar. Christmas Day is on or near January 7 in the Gregorian calendar. For example, Saturday January 7 2012 was Orthodox Christmas Day. More information can be found on the related link below.
The main Orthodox jurisdictions in the US are the Ecumenical Patriarchate, the Orthodox Church of America (OCA), the Moscow Patriarchate, the Antiochian Patriarchate, the Serbian Patriarchate and the Romanian Patriarchate. All of these jurisdictions are in communion with each other. They are not denominations, but simply "sister churches" of the one Eastern Orthodox Church.
They are called Eastern Orthodox Christians or just Orthodox Christians.
Technically there is no such thing as a "Greek Church." Most of the country of Greece is Orthodox. Orthodoxy is a world religion and can can be found in just about every country.
A ‘Greek Orthodox’ Christian is a Christian who comes under the Orthodox Church of Greece. In the rest of the world, he or she would be known as an Orthodox Christian. The name "greek orthodox" should not be used to describe Orthodox Christians in other countries outside of Greece. There is no nationality in the Orthodox Church. It is open to people of all backgrounds, races and cultures. Orthodox Christians in Japan are Japanese Orthodox, Orthodox Christians in Russia are Russian Orthodox, Orthodox Christians in America are American Orthodox, etc.