Anointing Oil is any type of oil used for anointing someone. Liturgical Christians and Jews have used oil to anoint people since the Exodus. Typically, one uses olive oil for its rich symbolism. Olive oil lighted their lamps, was used in cooking, among other things, giving the use of it a special place, since it was so vital to the Hebrew life. Many Christians feel oil represents the Holy Ghost.
Exodus 30 gives the special recipe for Holy Anointing Oil, the oil to be used when anointing kings, priests, and prophets. The recipe was never to be used except in those cases. Oil was also used to anoint other people, to honor them.
According to custom, the old anointing oil is to be mixed with the new anointing oil before being consecrated.
According to tradition, the very same oil from Exodus 30 still survived into the times of Jesus. This oil was then blessed by Jesus, and was buried, only to be found by a saint, and mixed with consecrated oil. This oil still survives today.
Catholics have three different types of anointing oil for three different purposes, all three blessed by the Bishop for special purposes during the Sacraments. Chrism is considered the holiest of the blessed oils, and is used for Confirmation. It is consecrated, as opposed to merely being blessed.
The Oil of Catechaums is blessed for use during baptism. Participants are anointed and then sprinkled or submerged with water. The Oil of the Infirm is blessed for use during Last Rites, to be used for healing during sickness.
Catholic oil typically has olive oil mixed with balsam, though some dioceses have variations in recipe, adding cinnamon or myrrh to the mixture. Some are elaborate, and others are quite plain.
The Orthodox have varied and very complex methods for creating oil for anointing. Typically, oil used during baptism is just olive oil blessed by the priest. Chrism used during chrismation uses an incredibly elaborate process, involving having several passages of scripture being read over the oil as it mixes for extended periods of time while the Bishop prays over it. There are several hundred ingredients put into it. During the Mystery of Unction, the Orthodox may request the mystery at any point in time for whatever illness, spiritual or physical. If any oil is left over from the process after the participant dies, it is sprinkled over the corpse before burial.
The Orthodox use "Myron," a special oil said to have been blessed by the Twelve Apostles while they were still on earth (In the case of a certain church, the story goes that Jesus blessed the oil). This Myron is put under special guard and added to the Chrism when it is made on Maundy Thursday.
Typically, liturgical Protestants will use anointing oil during the Anointing of the Sick. Lutheran, Presbyterian, Anglican, and Methodist churches all have a rite for this, but many of them consider it optional. Typically, the person is anointed and then prayed over. They usually just use olive oil.
Typically, the use of anointing oil is not used in the Evangelical circles. Some Baptist churches will anoint the sick upon request, but it is unusual. The exception to this rule is the Pentecostals, who frequently anoint themselves with oil to symbolize being anointed by the Spirit.