Yes, messianic claimants do not seem to have been uncommon in 1st century Judea. Jesus was not the first nor the last. The Jewish historian Josephus names three that preceded Jesus:

The first one is Judas, son of the bandit chief Ezekias whom Herod the Great had executed. Judas led a rebellion at Sepphoris in Galilee where he attacked its royal arsenal. He was probably a peasant bandit chieftain whose initial success raised him to the level of messianic claimant.

The second one was Simon of Perea, a slave of king Herod who led a rebellion that burnt down the palace in Jericho. He was executed by the Romans sometime between 4 and 15 AD. Simon is the Messiah of Gabriel's Revelation, a late 1st century AD stone tablet containing a collection of prophecies written in Hebrew.

The third messianic claimant mentioned by Josephus is Athronges in Judea who led a body of armed supporters who recognized him as king, against Herod Archelaus and the Romans, together with his four brothers. The insurrection may have lasted two years, 4-2 BC, and we do not know what happened to Athronges.

The prevalence of would-be messiahs in 1st century Judea can be attributed to many factors, but the main one being Jewish apocalypticism, that is, the belief that the end of times was near and that God would intervene in history in some form of cataclysmic way, and restore Israel to glory. There were many variants of these beliefs, but the prevalent one seems to have been that a king would rise (the messiah) who would destroy Israel's oppressors (Rome).

It should be noted that messianic movements are not unique to Judaism, though. John Dominic Crossan describes apocalypticism as a form of religious resistance among a group of people to an oppressing power, as "one possible response to a profound attack on cultural integrity", and notes that similar messianic movements rose across the near east (Persia, Egypt, Palestine) in the centuries earlier as a response to Hellenic imperialism, as well as in other parts of the world. Crossan uses, as one example, apocalypticism among Native Americans as a response to American imperialism in the 18th-19th century. The natives "undertook militant wars of religion like that led by The Prophet and Tecumseh, believed in messianic movements emphasizing high morality, like those in the Pacific Northwest, and even began proselytism among themselves, as in the case of Indian Shakerism or the Peyote cult".

Sources: Josephus, Jewish War; Josephus, Jewish Antiquities; Crossan, The Historical Jesus: The Life of a Mediterranean Jewish Peasant;

The concept of a coming mashiach ("anointed one") or Messiah arose in the period after Jewish territories in ancient Palestine had been overrun and conquered by a series of foreign powers, particularly after their conquest by Alexander the Great and their domination by his Seleucid successors.  After the brief period of independence resulting from the Maccabean revolt, the Jews came under the domination of the Romans, either directly or via their client rulers of the Herodian dynasty.

This was the political background to the rise of the idea of a Messiah - an "anointed one" who Yahweh would send to liberate Israel.  That was pretty much the only common element that Messianic expectation in the first century AD had.  Otherwise, ideas about this Messiah took a wide variety of forms.

 Some expectations were for a kingly Messiah - a descendant of King David who would unite Israel and lead the Jews to overthrow their oppressors.  Others were for a prophet Messiah - either Elijah returned from heaven or an Elijah figure who would unite Israel and usher in a new kingdom of Israel.  Others still expected a priestly Messiah - a perfect high priest sent by Yahweh to purify and liberate the land.  Other expectations were for a combination of these figures (as Jesus was seen to be) or for two or even three of these Messiahs in succession (as is indicated in some of the Dead Sea Scrolls).  There was also an expectation that the coming of the Messiah would usher in an apocalyptic intervention by Yahweh on earth, which would involve the wiping out of Israel's enemies, the judgment of the living and dead and the renewal of the earth in the "kingdom of God".  This was the core message of Jesus' teaching and it seems to have been his key belief.

There is a modern Christian idea that the only exception was for a purely political, warlike kingly Messiah and that the idea of a Messiah was widespread.  Both of these ideas are incorrect.  As noted above, there was a wide variety of expectations about who and what the Messiah was going to be.  But modern research also indicates that Messianic expectation was not as widespread as has often been assumed - it was more common in some social strata (especially in the lower classes) and arose periodically, usually in periods of social or political stress or upheaval.  While it's often claimed there were many Messianic claimants in the first century, we actually only have evidence of a handful.

Judas, son of Hezekiah - Around 4 BC Judas, in the confusion after the death of Herod the Great, this Judas who Josephus calls "head of the robbers" assaulted the royal palace in the new city of Sepphoris in Galilee, not far from what was to be Jesus' home village of Nazareth.  He seized the weapons in the armory there, stole all the money he could find and terrorized the surrounding countryside.  Josephus also says he had "an ambitious desire of the royal dignity", though whether he actually declared himself the kingly Messiah or whether others did so is not known.  It's not clear what happened to him, but the Roman governor of Syria, Publius Quinctilius Varus, later marched south to put down a number of uprisings in this year so it's likely he and his band were destroyed by the Romans in this campaign.

Simon of Peraea - At the same time, following the death of Herod, one of his servants called Simon of Peraea was acclaimed as king largely because, according to Josephus, he was " a comely person, of a tall and robust body".  He was crowned with the royal diadem and proceeded to burn and plunder a number of royal palaces.  Herod's former commander Gratus gathered a body of men and, reinforced by some Roman troops, fought a pitched battle against Simon's followers.  Simon himself fled the battle but was caught and beheaded.  Again, whether Simon or anyone else declared him the Messiah is unknown.

Judas the Galilean - Once the insurrections were put down, Herod's territory was divided between his sons, who ruled on the Romans' behalf as client kings.  The tetrarch Herod Archelaus proved a particularly ineffective ruler and in AD 6 he was deposed and Judea was placed under direct Roman rule.  A Galilean named Judas and a Pharisee called Zadok stirred up the people in reaction to this and began a revolt which was savagely repressed by Varus (see above), who Josephus says crucified 2000 people by the time his campaign was over.  Again, whether Judas claimed to be or was seen to be the Messiah is unclear, though a later speech depicted in Acts 5:36-37 has a Pharisee compare him to Jesus, so this is possible.

Jesus of Nazareth - Jesus' message of the coming and imminent apocalypse and the "kingdom of God" on earth that would follow was preached in the context of this atmosphere of repression and rebellion.  Unlike Judas or Simon, he does not seem to have preached a military uprising, but his message was that Yahweh was about to intervene in history and destroy the enemies of Israel.  Not surprisingly, when he took this message to Jerusalem and preached it under the Roman prefect's nose after instigating a riot in the Temple, he was arrested and crucified - the Roman punishment for sedition against the Empire.  Whether Jesus regarded himself as the Messiah or whether that was something his followers declared of him, either before or (more likely) after his execution is not clear.  But he was regarded as both a kingly Messiah and as a priestly Messiah as well.

Continued...

Follow up question:

Did Jesus himself even claim to be the Jewish Messiah?