The Jews have Hebrew. Muslims have Arabic. Hindus have Sanskrit.
For Christians, is there any holy language? Is there any holy language for Christians according to words of Jesus Christ and the apostles (from New Testament)?
Essentially, no: there is no language specified for religious use in Christianity.
From the early days of the Church, there was variety in religious language. The Western Church primarily spoke Latin (the vernacular) while the Eastern Church spoke Greek (again, the vernacular).
Various churches have languages that have special status, especially for liturgy. For instance, Latin still has a special status in the Latin Rite of the Roman Catholic Church; Old Church Slavonic is the liturgical language of the Russian Orthodox Church (among others); Syriac is used by the Maronite Church and the Syriac Orthodox Churches (again, among others). Hebrew and Greek obviously have a special importance as the languages of the Bible.
But none of these languages is as tightly bound to religious identity as Arabic, Hebrew or Sanskrit are to Islam, Judaism and Hinduism respectively.
(If I were to theorise, I would suggest that this is due to the nature of the development of these religions. Whereas those religions developed mainly in one culture, Christianity rapidly spread to and developed in multiple cultures. So it is not bound to one specific culture or language in the same way.)
Dogmatically no, there are no a holy language in global-christianity to do services or to speak in.
There was a heresy called Three-Language heresy, according to which it was said that the Christian church has only three languages to use in church: Hebrew (not Aramaic), Greek, and Latin. This "dogma" was based on the bible words [Luk 23:38 kjv]:
and [John 19:20 kjv]:
So some people are having said that since in the bible is referred to the only three languages, so the church can use the only those, even when it send a mission to other non-christian people, the first task is to learn the people to one of the languages, and then preach the gospel.
During the times of enlightment of slavs the pope condamned the doctrine as a heresy, and recognized the slavic alphabeth as holy language, however exactly this heresy has been persistently preached by German missionaries, and after a series of discussions sparked condemnation by the Slavic teachers.
However, we need to say that in arguments of the heresy advocates were non-empty. The point is that human is complex being, and he understands the meanings of words, of speach, in which he used not the only level to communication. So there are high style, low or "trade" style of speach, and of course holy level. And this level of course may be used by a human to the prayer, and if human don't use the style, all his life is undergoing to desacralizations. It is just one of ascetics rule. For example, the Solun brother had known this rule, and created the church-slavonic language as an artificial one based on the Macedonian dialect of old-slavic language of that time.
In present time we see the variouse languages which is used as a sacral language of a variuos churches even non-Orthodox, or Catholic.
The Bible affirms in many places that God loves all nations, tribes, and tongues/languages.
At the very inception of the church at Pentecost, God worked so that people heard the message of Christ in their own languages.
In the Book of Revelation, the prophecy is that there will be believers from every language on earth.
Furthermore, the concept of all nations runs throughout the Scriptures like a scarlet thread. Implicit in individual nations is individual languages as well, as God actually created the languages in Genesis 11. To list just a very small fraction of the verses:
So, no, there is no sacred language in Christianity. The Old Testament is almost entirely Hebrew, yet Jesus likely spoke in Aramaic, and His words were recorded in Greek.
Because of the belief there is no sacred language, but God is the God of all people who speak any language, Bible translation has been a primary investment throughout the world. In fact, it may be that the translation of the Bible into every spoken language could be completed by the end of this century.
Although I am not sure that this is what you are asking, but there is the speaking in tongues which Paul made mention of in 1st Corinthians, and there are these:
I see good answers so far, but I'll still add mine.
A Holy language to speak to each other? I don't think so. However, the scripture says
We can talk to God in a language that only He (not even ourselves) understand, possible through the Holy Spirit.