AP: There are verses in the Gospels that tell us what language Jesus spoke. Mark 5:41 reads, “Taking the child by the hand, [Jesus] said to her, ‘Talitha kum!’ (which translated means, ‘Little girl, I say to you, get up!’).” Mark 7:34 reads, “And looking up to heaven with a deep sigh, [Jesus] said to him, ‘Ephphatha!’ which means, ‘Be opened!’” Mark 14:36 records Jesus saying, “Abba! Father!” And, from the cross, we see in Mark 15:34 Jesus crying out in a language other than Greek: “At the ninth hour Jesus cried out with a loud voice, ‘Eloi, Eloi, Lama Sabachthani?’ which is translated, ‘My God, My God, why have you forsaken me?” From these alone we can see that Jesus spoke Aramaic. Although there are some scholars who argue that Jesus could have spoken Hebrew as his native tongue, and that Hebrew never ceased to be spoken by the majority of Israel’s population, the majority believe the Jewish people in Jesus’ day spoke Aramaic in Judea and Galilee. The switch from Hebrew took place gradually over time, beginning in the sixth century B.C., when Israel came under the rule of the Persian Empire. Aramaic was the lingua franca of the Western Empire. Jesus, therefore, must have spoke and preached in this language not only Galilee, but also in Jerusalem, where the inhabitants, and most of the pilgrims, called the Aramaic language their mother tongue as well. However, many scholars also believe that Jesus could have known Hebrew too, especially since Jewish people who studied the Scriptures maintained a working knowledge of the language, being able to read the sacred text and also carry on discussions about the meaning of its passages. In the end, though, there is insufficient data to land one’s plane definitely.
It is generally believed that given the proximity of Nazareth to Sepphoris and Tiberias, which were full of Greek-speaking people, it is also reasonable to think that Jesus must have had some knowledge of Greek, at the very least for professional reasons.
TWH: The verses that Antonio points out above (Mark 5:41; 7:34; 14:36; 15:34) are evidence that Jesus spoke Aramaic. We also know that Jesus read from the Hebrew scrolls in the synagogue (e.g., Luke 4:16ff.), and, therefore, had a working knowledge of the Hebrew language. Given the fact that Jesus and his family worked in construction ("building"), Jesus and his family probably knew and used Greek regularly. (Greek was the koine of the empire of Jesus' day.)
My own two cents: I think that Jesus was trilingual.