One famous claimant was Simon bar Kochba, a mid-2nd century rebel against Roman rule who led the Second Jewish Revolt against Rome in the days of Hadrian. He was supported by the great scholar Rabbi Akiba, who recognized Simon as the Messiah, but the ensuing Roman victory ruined Simon's messianic credibility and culminated from the Jewish exile from the province Hadrian renamed Palestina.

A major messianic claimant was Shabbatai Tsvi, in the 17th century. He was originally from Turkey, and began telling people he was the messiah at a fairly young age. His claims spread pretty widely through the Jewish community, to Europe.

For a couple decades he traveled around claiming he was the messiah, gaining followers. He did all sorts of weird religious things, such as declaring fast days to be days of celebration, eating meat only allowed to be given as a sacrifice, etc. While he definitely had opponents, he was able to get the story to spread pretty widely that he was the messiah.

Eventually he attracted the attention of the Ottoman government, which was sorta inevitable since he was getting so popular. He was forced to convert to Islam, and he died in relative obscurity. There remained a small sect loyal to him until relatively recently.