One of the features of Mark's Gospel is the fact that Jesus keeps his identity as Messiah a secret. The demons recognize him as the Holy One of Israel from the beginning but he silences them. But even near the end of his time on earth, when his disciples finally acknowledge him as Christ, he tells them to keep it a secret. It is an issue that's been around for a century: Why does he keep it a secret?
William Wrede famously suggested in 1901 that the reason Mark has Jesus keep his identity a secret is because Jesus never actually claimed to be the Messiah. His suggestion was that the early Christians found themselves in the awkward position of believing Jesus to be the promised king when he himself had never claimed that himself. The solution was to argue that Jesus had known he was the Messiah but had kept it a secret.
There are, however, two strong historical arguments that Jesus did in fact believe himself to be the Messiah. The first is that he designated twelve disciples. The tradition may vary a little on the precise names of the twelve, but all the layers of tradition consistently give the number as twelve. This is true from Paul (1 Cor. 15:5) to John (e.g., 6:70; 20:24) to the Synoptics (e.g., Mark 3:13-19). The number is surely symbolic of the twelve tribes of Israel. And since Jesus does not include himself among the twelve, he is surely the king of the tribes.
Jesus' entrance into Jerusalem seems another strong indication he thought himself king. His entrance at the beginning of Passion Week seems deliberately calculated to echo Zechariah 9:9. Jesus comes riding into town on a donkey, with the crowd laying palm branches down before him. Certainly there are other possible explanations. Some might say this story is a later invention created from certain verses in the Old Testament. Another might suggest that Jesus was simply mocking the pomp of Herod Antipas' supposed entrance to the city.
But the connection to Herod is highly speculative--Luke is in fact the only Gospel that says he was even there. And in this case it seems far more likely that Old Testament Scriptures would be used to enhance a historical event rather than to invent one. Surely the most likely historical scenario is that Jesus' entrance to Jerusalem on this occasion was memorable. And the fact that Mark, the earliest Gospel, doesn't make the connection with Zechariah, suggests that he did not invent the donkey to make it look like Jesus was fulfilling the Scripture in Zechariah, that Jesus was implicitly claiming to be king.
I might mention a third item of interest. The Gospel of Mark seems to connect Jesus' baptism with the beginning of Jesus' messianic activity. The voice from heaven in Mark speaks only to him: "You are my beloved Son" (1:11), where Son of God is a royal title, the title of a king. We get the impression that something changed for Jesus at the baptism. Was it even at this point that Jesus in his human understanding realizes that he was the promised king?
So if Jesus did understand himself to be the promised Messiah, why didn't he publicize it? A strong possibility is that, at the very least, Jesus had no intention to lead an armed revolt against the Romans. That is of course how the crowds would have understood Messiah. If Jesus had gone around claiming that he was the coming king, then all the low life of Galilee would have grabbed their swords.
Indeed, it does not even compute for Peter that a messiah would die. The Messiah won't die. He'll win. He'll kick the Romans out of town and restore the kingdom to Israel (Acts 1:6). In a sense, Jesus wasn't the messiah they were looking for. It thus made perfect sense for him to keep his destiny close to his chest.
But surely the crowds suspected it anyway. Indeed, although Jesus also tries to keep his healing ministry somewhat low key, those he heals don't listen to him when he tells them to keep things quiet (e.g., Mark 1:44-45). Jesus seems to be waiting for God's timing. He tries to keep his activities and destiny hush hush because he knows the timing the crowds would want.
 So E P Sanders, Jesus and Judaism.