Most, although not all use bread with yeast. Armenian Apostolic and a few others do not use yeast bread.
Eastern Rite Catholics also use the same bread as the Eastern Orthodox Churches.
The interpretation of the Bible held in the East, is that the Last Supper took place on the Eve of the Passover, so unleavened bread was not required. The Latin Rite interpretation is that it was the Passover Meal, at which the Eucharist was instituted. Since the Church has not officially defined if it was one or the other, both are permitted by Church Law. The Laws of the Latin Rite state that only Unlevended bread is licit, (Legal) for use in the Eucharistic Celebrations of the Latin Rite. Eastern Rite Catholic Churches (and the Orthodox equivalents) have their own Canon and Liturgical Laws according to the Rite. The manner that they distribute Communion, (In many Eastern Liturgies, the priest puts the Consecrated bread into the chalice and administers both with a spoon.) In others, the priest administers the consecrated host, or consecrated bread which he inticts, or dips into the chalice.
One thing that each of us needs to realize is that the Eastern Rite Catholic Liturgies, as just as much the Mass as any Latin/Western Rite Catholic Liturgy. At every Mass, we stand at the foot of the Cross. At every Mass, Jesus is the primary priest, who is present for us, both in the Eucharits, and through His minister, the priest.