Doctrinally, not very much. The Orthodox churches and the Roman Catholic Church split over the authority of the Holy See of Rome, or the Pope. The Orthodox church thought to Pope was given too much Authority. The only other major difference between the two is the Holy Trinity. The Orthodox believe the divinity of the Holy Spirit comes only from God, the Father. The RC believes the Holy Spirit comes from the Father and Son. There are other minor differences, but only a religious scholar could relay describe what they are.
They split apart in 1054 CE - before that, they were one church with four popes or patriarchs. Orthodox are not that different from RC really. One obvious difference is the orthodox allow priests to marry, but if they do they can't become bishops.
Different Popes since the Great Schism (both sides believe themselves to be in apostolic succession). Also, the Orthodox believe in Consubstantiation (bread and wine coexist with the Body and Blood of Christ) and Roman Catholics believe in Transubstantiation (the bread and wine BECOME the Body and Blood of Christ).
The Orthodox traditionally said mass in Greek, and the RC traditionally said mass in Latin. Also, I don't think priestly celibacy is required by the Orthodox Churches.
The Eastern Orthodox Church split from the catholic church in 1054AD. They reject the authority of the pope and do not enforce any Catholic doctrines made after 1054AD. They also strongly belief they are the true church, thus persecute other religions in countries that are primarily orthodox IE Greece. Despite these differences, they are very like Catholic IE. they worship idols (Commandment #2), they worship on Sunday (Commandment #4)
This is a big question, and it would take a book to list all the differences. The following are just a few.
1. The Roman Catholic liturgy was traditionally in Latin. The Orthodox Churches use other languages, including Greek, Russian and Syriac.
2. The Orthodox Churches allow married priests. The Roman Catholic Church (with very rare exceptions) does not.
3. The Orthodox and Catholic Churches use different ways to calculate the date of Easter, so that in most years they end up celebrating the feast on different days.
4. The Catholic Church recognizes the Pope as having supreme spiritual authority on earth. The Orthodox churches dispute this.
5. The Catholic Church recognizes a number ecumenical councils which the Orthodox Churches do not (egg Trent, Vatican I, Vatican II).
6. The Catholic Church accepts the 'foliage' clause (Google it) in the Nicene Creed. The Orthodox churches consider it to be an unjustified addition.
Having said this, the things which unite the Catholic and Orthodox churches are greater than those that divide them. Both are in broad agreement on nearly all major points of doctrine and most of the differences between them are cultural,. Cultural differences are not barriers to unity, as there are already many churches (egg Maronite Catholic Church, Chaldean Catholic Church, etc) which are culturally distinct from the Roman Catholic Church yet in a full state of unity with it.
How was the eastern orthodox church different than the roman catholic church?
