People who live in a country that has one dominant language are likely to ask "What language did Jesus speak?" People who live in a country where multiple languages are spoken are likely to ask "What languages did Jesus speak?" Our cultural background can influence even how we ask this question.

The place where Jesus was crucified was near the city, and the sign was written in Hebrew, Latin, and Greek, so that many people could read it. (John 19:20, NLT)

Many of the Jews read this inscription, for the place where Jesus was crucified was near the city, and it was written in Aramaic, in Latin, and in Greek. (John 19:20, ESV)

According according to archaelogical research, at the time of Jesus, Hebrew, Aramaic, Greek, Latin were all commonly used. The inscriptions on buildings, tombs, pottery, and documents suggest a reasonably even split between all three languages. Some scholars, especially prior to modern archaelogical discoveries assumed that Aramiac was the dominant language and Heberw was mostly limited to religious use in religious settings. The most up to date publications on this topic suggest that Hebrew was more common than was previously assumed.

Did Jesus speak Greek?

We know that Jesus grew up in Nazareth, not far from Sepphoris, the capital of Galilee. It was a trade and commerce hub, and influenced by Greek thought. Jesus may not have spoken Greek at home, but it is reasonable to assume that Jesus developed some capacity to speak Greek. Especially when you consider evidence in the Biblical Text itself.

The conversation between Jesus and Nicodemus (John 3) contains a clear confusion over a single Greek word, which can mean both "born again" or "born from above." This confusion only makes sense if the conversation occurred in Greek.

The conversation between Jesus and the Roman Centurion in Capernaum (Matthew 8, Luke 7) is also informative. A Roman Centurion would likely have an ability to communicate in Latin and Greek. It is unlikely that the Centurion had the ability to speak Hebrew or Aramaic. The natural language of communication between Jesus and a Centurion would have been Greek.

Did Jesus speak Hebrew?

The Dead Sea Scrolls (DSS), the Mishnah, and the Bar Kokhba letters suggest that Hebrew was not limited to religious settings. They suggest Hebrew was regularly used in every day setttings extending into at least the 2nd century A.D. The Dead Sea Scrolls (DSS) are ancient manuscripts that were discovered between 1947 and 1956. They are predominantly Hebrew and can be dated between the 3rd century BC and the 1st century AD.

The Bar Kokhba letters are evidence of Hebrew being used in regular communication, andc are dated in the 2nd century. These letters are correspondence between Bar Kokhba and his subordinates.

Did Jesus speak Latin?

Latin was the official language of the Roman army. Roman soldiers likely had at least a limited capacity to speak and understand basic Latin. A non-Native Roman soldier living in Israel was quite possibly comfortable speaking Latin. A Roman soldier who did not speak Latin natively probably aquired some limited functional ability to speak and understand Latin. It is most likely that when Jesus spoke to a solder, or to Pilate, that the common language between the two was Greek. But it is not possible to rule out that Jesus had at least some ability to understand and speak basic Latin.

Translation of Scripture

There is a Greek phrase found in the Greek New testament, meaning "The Hebrew language" or "The language of the Hebrews" (τῇ Ἑβραΐδι διαλέκτῳ.)

And when they heard that he was addressing them in the Hebrew language, they became even more quiet. (Acts 22:2, ESV)

Was the "Hebrew language" Hebrew or Aramaic? The NLT translation chooses to avoid answering the question by removing the word "Hebrew" from the English translation.

When they heard him speaking in their own language, the silence was even greater. (Acts 22:2, NLT)

The NLT adds a footnote suggesting that this verse could be refering to the Hebrew or Aramaic language. Effectively leading it up to the reader to decide for themselves what the language of the crowd was.

Those of us from a country that speaks one language may be inclined to assume that there is only one correct answer. However those of us from a country that speaks multiple languages natrually assume that Jesus spoke multiple languages, possibly to different levels of competence. The evidence suggests that it is more than likely that the language Jesus spoke depended on the context of the conversation. To a Greek speaker he likely spoke Greek. To a Hebrew speaker he likly spoke Hebrew. To an Aramaic speaker he likely spoke Aramaic. Who knows, perhaps, there is even a small chance that Jesus understood and spoke at least a small amount of Latin also.