Within the Jewish tradition, the most important was almost certainly Simon bar Kokhba, who led the Third Jewish Revolt (132–136 CE), which was the last major Jewish-Roman war and ultimately led to the Jews being banned from Jerusalem (except on the holiday of Tish b'Av). The Temple had already been destroyed in the Great Jewish Revolt (66-70 CE). Many people, including apparently people like R. Akiva who later became important to Rabbinic (post-exilic) Judaism, believed that Simon bar Kokhba was the promised Messiah, who would bring about the messianic age.

He's undoubtedly the most important (besides John the Bapist and Jesus, in the period before Muhammed), but Livius.org has a list of Messiah claimants (or rather, people that other people claimed were the Messiah, even if the people themselves maintained a policy of strategic ambiguity), including sixteen others from the period 4 BCE to 600 CE that show up in our primary sources. The most useful thing about the site is that by clicking on the name, it takes you directly to the a page on them with the primary source information--mainly it comes from Josephus, who wrote the Jewish War and Jewish Antiquities. The ones up to ~75, when Josephus wrote The Jewish War (Jewish Antiquities followed in ~94), are more numerous than the ones after. While this may have been a particularly topsy-turvy time given to following prophets and messiah claimants, this also may reflect that we have a really good source for the period up to this point (namely, Josephus, with some additional stuff being found in the Christian New Testament and also in other historians, like Tacticus), and we have more scattered sources after (the Talmud, Eusebius's History of the Church, other Christian apologetics, etc).

And that's just among the Jews. There were many other cultic movements that were able to gain substantial followings, though they generally claimed to build off a much older tradition--we generally lump them together today as the Late Antique Mystery Religions (it was long fashionable to put early Christianity in this context as well, though I don't know if this is as common as it once was). These were generally not named after prophets, but gods or demigods who the initiates worshipped in particular, using secret rituals available only to those who had been initiated. You have mysteries of Isis, Dionysus, Attis, Cybele, Demeter & Persephone (the Eleusinian Mysteries), Mithras, Sabazios, and others. While they all claimed to be much older than this period, it's very much unclear whether any were (though I'm not an expert on the subject). Many of them developed around exotic, Eastern gods (Isis, Attis, Cybele, Mithras, and Sabazios from the above list), which were probably introduced to the broader Roman public through people I'd be comfortable labeling "prophets". You also have similar groups with more explicit prophetic intercession, like Manichaeism (which drew strongly from the Zoroastrian tradition, but also drew from Christianity and maybe beyond).

So, in short, the Roman Empire not only let trade of goods flourish, but it also allowed the trade of ideas and traditions to flourish which, at its height, led to a flourishing of lots of prophetic followings. Then, as now, ideas from the East were seen as particularly fashionable and exotic and full of mystical power. The neighboring Sassanid Empire, though Zoroastrianism by definition was less open to borrowing than Roman religion, may have experienced similar things (c.f. Mani, Zurvanism), but I know less about them. Most of these groups, however, left no traces in the historical record.

I'm extremely surprised that nobody has mentioned the prophet and founder of the worldwide religion Manicheeism, Mani.

This question almost seemed custom phrased for that answer.

Mani, born in Persia, roughly 216 CE was the founder of Manicheeism, which at one point had a decent shot at being the dominant religion of the World, before being eventually defeated by Christianity, Zoroastrianism, Islam, and even the eastern religions it encroached upon in India and China. It was basically gone by the end of the 9th century.

Edit: I just noticed that /u/yodatsracist did mention Manicheeism, albeit parenthetically. I figured it deserved quite a bit more attention than that.

So far all examples given have focused on religions other than Christianity. Within the spectrum of Christianity the three prophets Montanus, Prisca and Maximilla attracted a decent following (including Tertullian) in Africa and Asia during the late second century and even in the sixth century Justinian still includes the Montanists in his anti-heretical laws (CJ I,5,18-20).

(Montanism has nothing whatsoever to do with Ultramontanism, the similarity of terms is entirely coincidental.)