Significant findings and study have revealed that Matthew was originally written in Hebrew.
Papias, the disciple of John, stated this fact plainly, and it was alluded to by many early church historians as well.
In the 4th century, Eusebius, the Bishop of Caesarea, also stated that he saw the Hebrew Matthew in Caesarea Philippi.
Another gospel has been located in Hebrew, but has not yet been secured for study, so more on that cannot be disclosed at this time.
Many people, groups and ministries have tried to claim that the gospels were written in Aramaic, but this claim does not hold up to careful scrutiny.
The Aramaic script we have today is not even used in the Aramaic church in Israel.
The most well known Aramaic resource, the Peshitta, is very obviously translated from later Greek texts, as evidenced by the fact that it contains insertions that are not found in earlier texts.
Greek is the oldest text available for the other gospel records, so unless and until we find evidence to the contrary, they appear to be originally written in Greek.
This makes sense, as Greek was the lingua franca for the entire empire, which stretched from Macedonia to the Indus River and down to Ethiopia.